Calculus Questions

Pierce Manufacturing determines that the daily revenue in dollars from the sale of x lawn chairs is R x 0 004x 0 a What is the current daily revenue b How much would revenue increase if 75 lawn chairs were sold each day 0 05x 0 5x Currently Pierce sells 70 lawn chairs daily c What is the marginal revenue when 70 lawn chairs are sold daily d Use the answer from part c to estimate R 71 R 72 and R 73

The function f x y z xyz 1 2 has an absolute maximum value and absolute minimum value subject to the constraint x y z 4 with x 20 y 20 and z 20 Use Lagrange multipli to find these values The absolute maximum value is 4 4 3 3 The absolute minimum value is 0 GEER

48 67 Find the four second order partial derivatives for f x y 5x y 4xy7 45 f 11

A company s marginal cost function is MC x x 1 2 5 where x is the number of units If fixed costs are 23 250 find t company s cost function C x

Find the absolute extreme values of the function shown below 10 4 Absolute Minimum Value 5 10 x

Let R x C x and P x be respectively the revenue cost and profit in dollars from the production and sale of x items If R x 7x and C x 0 005x2 2 6x 60 find each of the following a P x b R 200 C 200 and P 200 c R x C x and P x d R 200 C 200 and P 200

8 Identify which of the following trig functions represents that of a sin cos tan cot csc and sec function f 4 2 A U 44

A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the soil measured in appropriate units is KN 9 Y where k is a positive constant What nitrogen level gives the best yield N

A box with a square base and open top must have a volume of 62 500 cm Find the dimensions of the box that minimize the amount of material us sides of base cm height cm

A poster is to have an area of 210 in2 with 1 inch margins at the bottom and sides and a 2 inch margin at the top Find the exact dimensions that will give the largest printed are width height in in MY NOTES

Explain why Newton s method doesn t work for finding the root of the equation x3 3x 9 0 if the initial approximation is chosen to be x 1 f x x 3x 9 f x in trying to Select by zero If x 1 then f x and the tangent line used for approximating x2 is Select Attempting to find x2

6 66 Points DETAILS SCALCET8 4 7 021 Find the point on the line y 5x 2 that is closest to the origin x y

If 10 800 cm of material is available to make a box with a square base and an open top find the largest possible volume of the b cm3

3a Give a definition for the piecewise function shown below 5 3b Identify the discontinuities of the function 0

Sketch the graph of a function f that is continuous on 1 5 and has the given properties Absolute maximum at 5 absolute minimum at 2 local maximum at 3 local minima at 2 and 4 3 3 25 O s 0 5 3 2 5 2 15 1 2 3 4 5 6

Find the absolute minimum and absolute maximum values of f on the given interval f x 0 6 x 2 x 4 absolute minimum value absolute maximum value

10 Solve for side length a in the triangle below Round your answer to one decimal place X 35

Find the critical numbers of the function Enter your answers as a comma separated list Use n to denote any arbitrary integer values If an answer does not exist enter DNE f 0 4 cos 0 2 sin 0 x

Find the critical numbers of the function Enter your answers as a comma separated list If an answer do not exist enter DNE f x 8x 12x 48x H

Explain the difference between an absolute minimum and a local minimum There is no difference O A function f has an absolute minimum at x cif f c is the largest function value on the entire domain of f whereas f has a local minimum at c if f c is the largest function value when is nea C A function f has an absolute minimum at x c if f c is the smallest function value when a is near c whereas f has a local minimum at cif f c is the smallest function value on the entire domain of f A function f has an absolute minimum ata cif f c is the largest function value when z is near c whereas f has a local minimum at cif f c is the largest function value on the entire domain of f OA function f has an absolute minimum at x cif f c is the smallest function value on the entire domain of f whereas f has a local minimum at cif f c is the smallest function value when z is

Car s speed km h 80 60 40 20 0 2 4 5 6 7 8 Distance from home km 12 A school vending machine sells cartons of milk and juice On a typical day No cartons are sold between 7 A M and 8 A M or from 5 P M onward The machine has a capacity of 100 cartons At 7 A M it is three quarters full From 8 A M to 10 A M 10 15 A M to noon and from 1 P M to 3 P M the students are in class The machine is filled at 11 A M and at 4 P M Sketch a graph of the number of cartons in the vending machine as a function of time Explain what each section of the graph represents

Vrite an equation of a circle with diameter AB A 3 3 B 17 17 Choose the correct answer below A x 10 2 y 10 98 OC x 10 y 10 98 E x 10 2 y 10 3 OG x 10 y 10 98 OB x 10 y 10 OD x 10 y 10 OF x 3 y 3 1 OH x 17 2 y 17

Find the slopes of the curve y y2 x at the two points shown here Q Q 194 3 2 3 3 The slope of the curve y y x at the point Type an exact answer using radicals as needed The slope of the curve y y x at the point Type an exact answer using radicals as needed 3 4 is is

nd the slopes of the curve y4 y2 x at the two points shown here Ay 3 1 2 oo 3 4 The slope of the curve y4 y2 x at the point Type an exact answer using radicals as needed The slope of the curve y4 y2 x at the point Type an exact answer using radicals as needed 3 4 1 2 is 3 3 2 is

Write an equation of a circle with diameter AB A 3 3 B 17 17 Choose the correct answer below OA x 10 y 10 98 OC x 10 y 10 98 O E x 10 y 10 3 O G x 10 y 10 98 OB x 10 y 10 OD x 10 y 10 OF x 3 y 3 17 OH x 17 y 17

Find the exact solutions of the equation in the interval 0 2 sin 2x cos x 0 X X X X smallest value largest value

Solve the equation for x Use n as an integer constant cos r cos r 1 0 X X smaller value for n 0 larger value for n 0

Find the value of x x 0 X X 3

Find all solutions of the equation in the interval 0 2m algebraically Use the table feature of a graphing utility to check your answer numerically Enter your answers as a comma separated list 3 sin x 2 sin x

Find all solutions of the equation in the interval 0 360 Enter your answers as a comma separated list cos x 1

Find the area of the shaded region Use 3 14 m 26 m r 13 m 26 m

Determine algebraically whether the given function is even odd or neither g x 3x 5 ONeither O Even Odd

Find the area shared by the circle r2 4 and the cardioid r 4 1 cos 0 The area shared by the circle and the cardioid is Type an exact answer using as needed

Find the length of the spiral r 02 0 0 45 The length of the spiral is Simplify your answer

Find the area of the region inside one leaf of the three leaved rose r 3 cos 30 The area of the region is Type an exact answer using as needed

Suppose the derivative of a function f is f x x 2 x 5 x 6 On what interval is f increasing Enter your answer interval notation

Question Given the function 3x 9 X 5 use a linear approximation of f x at x 4 to approximate the value of f 4 1 Provide your answer below f x

Graph the polar equation r 5 cos 50 O A 10 10 10 10 Q OB 10 10 10 TT 10 O C 10 AT 1 TTTTT 10 10 10 O D 10 10 10 10

Use the graph of the rational function shown to complete the statement As x o f x 10 8 6 4 10 8 6 4 2 3 Ay 10 2 4 6 8 10 O A 1 OB o OC 0 OD 0

Given that x and y are functions of time find the indicated rate of change dy dx Find when x 2 and dt dy dt 3 given that x4 y4 97 dt Round to two decimal places as needed

HQ Four Quadrant Ordered Pairs B C 3 3 G E C Z 4 3 2 4 S Write the ordered pair for each given point 8 4 9 W 11 I 10 12 Z 2 2 2 1 1 2 4 4 5 8 Tell what point is located at each ordered pair 1 3 7 3 6 4 2 8 7 4 9 7 8 9 5 8 9 6 3 8 13 G 14 T Plot the following points on the coordinate grid 17 O 7 4 19 V 2 5 18 F 3 6 20 A 2 9 W X messa 21 Y 1 6 22 U 2 5 1 2 6 1 D 7 4 4 8 1 3 15 D 8 6 16 J 3 1 23 M 1 5 24 N 8 8

Estimate the error if P x 1 2 X is used to estimate the value of cos x at x 0 6 2 Error Simplify your answer Round to seven decimal places as needed

A quantity x is distributed through a population with probability density function p x and cumulative distribution function P x Decide if the statement is true or false If p 12 2 then half the population has x 12 True False

Which of the following functions makes the most sense as a model for the probability density function representing the time in minutes starting at t 0 that the next customer walks into a store Op t 3e 3t for t 0 Op t e 3t for t 0 O O p t f for 0 t 5 5 p t cost 0 t 2 e 2n t 2n

Find the slopes of the curve y y x at the two points shown here 4 coll Ay 0 Q The slope of the curve y y x at the point Type an exact answer using radicals as need

Find the value of x 2 X Do not include the degree symbol in your answer Round to the nearest degree as need

Find the critical points of the following function Use the Second Derivative Test to determine if possible whether each critical point corresponds to a local maximum local minimum or saddle point If the Second Derivative Test is inconclusive determine the behavior of the function at the critical points 2 2 f x y 4x 6xy 4x 1 What are the critical points Type an ordered pair Use a comma to separate answers as needed

A delivery company requires that any box delivered must have a length plus girth distance around totaling no more than 120 inches Find the dimensions of the box with maximum volume that can be sent The dimensions of the box with maximum volume that can be sent are Simplify your answer Use a comma to separate answers as needed inches CE

The volume of a right circular cone with radius r and height h is V h 3 a Approximate the change in the volume of the cone when the radius changes from r 5 5 to r 5 9 and the height changes from h 4 20 to h 4 11 b Approximate the change in the volume of the cone when the radius changes from r 5 17 to r 5 16 and the height changes from h 14 0 to h 13 93 a The approximate change in volume is dV Type an integer or decimal rounded to two decimal places as needed b The approximate change in volume is dV Type an integer or decimal rounded to two decimal places as needed LO

12 5 Compute the directional derivative of the function g x y sin x 5x 4y at the point P 1 3 in the direction 5 13 13 The directional derivative is Type an exact answer using x as needed CO Be sure to use a unit vector for the direction vector