Calculus Questions

Let h x f x g x If f x 4x 3x and g x ln 3x 1 what is h x

Let h x f x g x If f x 2x 2x 3 and g x x 3x 4 what is h 1 Provide your answer below h 1

Let h x f x g x If f x x 1 and g x x 4x 2 what is h 2 Do not include h 2 in your answer For example if you found h 2 7 you would enter 7

Suppose you are given a formula for a function f a How do you determine where f is increasing or decreasing b How do you determine where the graph of f is concave upward or concave downward c How do you locate inflection points

Let z z 13 2x 6 Find an equation for the tangent line to the graph of fat z 4 Tangent line y

Find the derivative of g x 87 U 26

Let f x 5x cos 5x 3 f x

Find the average value of f x x on the interval 2 6 3

Find the average value of f x 2 sin x 6 cos z on the interval 0 Average value

Let f x 2 sin cos

If f x then x 0 t 4t 7 dt

Local Maximum or Minimum on an Interval f x 2x 9x 4 x 6x 3 x 2x 16 x 2 3x 4x Sketch 36x 20 Interval 1 x 5 4 x 8 0 x 14 3 x 4 1 J 4 Endpoints 0 14 3 4 5

A carpenter is building an open box with a square base for holding firewood The box must have a surface area of 8 m What dimensions will yield the maximum volume

Year between 2001 and 2004 Sales millions of dollars 1998 1999 201 219 2000 2001 2002 2003 2004 2005 2006 233 245 251 251 252 243 233 e table above gives the annual sales in millions of dollars of a product from 1998 to 2006 What was the average rate of change of annual sales between 2001 and 2002

Based on the graphs of f x and g z below answer the following questions You should not approximate any of your answers K 2 2 4 0 5 2 6 1 6 9 4 9 2 9 a What is the average rate of change of f x over the interval 2 2 x 6 1 b What is the average rate of change of g x over the interval 2 2 x 6 1 8 0 9

At the start of a trip the odometer on a car reads 20809 miles At the end of the trip 15 hours later the odometer reads 21370 miles What is the average speed the car traveled during this trip miles hour

Find the intervals where the function y f x whose graph is given below is increasing and where it is decreasing and find the value of the absolute minimum Increasing Decreasing 1 0 Click on graph to enlarge Absolute minimum y help intervals help intervals help numbers

Find the intervals where the function y x 1 1 whose graph is given below is increasing and where it is decreasing and find the value of the absolute minimum Increasing Decreasing Click on graph to enlarge Absolute minimum help formulas help formulas help numbers

Find the average rate of change for f t 4t 9 over the interval 2 2 h help formulas

Find the average rate of change for f x 5x 3x over the interval 4 5 Be sure to simplify the answe help numbers

a The graph of y f x is shown Draw the graph of y f x Ex X

b The graph of y g x is shown Draw the graph of y g K 8 6 4 8 6 4 2 6 6 8 X X 2

The decay rate k for a particular radioactive element is 2 1 where time is measured in years Find the half life of the element

Score 11 17 11 17 answered Question 5 V A phone company charges for service according to the formula C n 19 0 04n where n is the number of minutes talked and C n is the monthly charge in dollars The rate of change in this equation is The initial value in this equation is Question Help Video Message instructor Select an answer Select an answer O

Score 11 17 answered Question 6 If f x is a linear function f 1 3 and f 3 5 find an equation for f x f x Question Help Video Message instructor

100x 0 4x2 where x is the The total revenue for Fred s Estates LLC is given as the function R x number of rooms rented What number of rooms rented produces the maximum revenue

Question 2 Is y 98 10 increasing or decreasing increasing O decreasing Question Help Message instructor

Identify the quadrant in which the following point is located 2 3 1 2 Choose the correct quadrant below that the given point is located quadrant I O quadrant III O quadrant IV O quadrant II

Score 2 8 2 8 answered Question 7 Find the area of a triangle bounded by the y axis the line f x 6 f x that passes through the origin Area Question Help Video Message instructor 5 7 and the line perpendicular to

Find the time of flight range and maximum height of the following two dimensional trajectory assuming no forces other than gravity The initial position is 0 0 and the initial velocity is vo uo vo ov 40 70 m s The object is in the air for Type an integer or decimal seconds rounded to two decimal places as needed The range of the object is meters Type an integer or decimal rounded to two decimal places as needed The object reaches a maximum height of meters Type an integer or decimal rounded to two decimal places as needed SITE

Question 1 In 2002 a school population was 1933 By 2006 the population had grown to 2189 1 How much did the population grow between the year 2002 and 2006 students 2 How long did it take the population to grow from 1933 students to 2189 students years 3 What is the average population growth per year P Select an answer 4 What was the population in the year 2000 students 5 Find an equation for the population P of the school t years after 2000 6 Using your equation predict the population of the school in 2012

Question 5 You are choosing between two different cell phone plans The first plan charges a rate of 22 cents per minute The second plan charges a monthly fee of 34 95 plus 12 cents per minute How many minutes would you have to use in a month in order for the second plan to be preferable Round up to the nearest whole minute minutes Question Help Video Message instructor

e 2 t 3 e 8 The answer above is NOT correct Find the solution to satisfying dy dt e t 3 e8 2y View y 4 3

c 5 pts Find the equation for the tangent line to f x at the point 1 3 x 2 obr tangent V

Consider the function f x x2 4x 8 a 5 pts Use the limit definition of derivative to find f x You must show all your work Tim 116 lim X h 4 8 X 4X 8 h 2 X 2th th 48 8 X 4x 8 2 xh th h 140 lim 70 n lim h 0 2X 2 X how b 5 pts Find the x values where the tangent line to f x is horizontal You must show all your work 2 f x 2 4 2 8 0 4 8 8 0 set fc then Solv 4 0 4 F X 4 f a

Chariots Mecklenburg Schools Practice Small group Instruction 1 Lin and Noah are solving the equation 7 2 2 91 Lin starts by using the distributive property Noah starts by dividing each side by 7 a Show what Lin s and Noah s full solution methods might look like b What is the same and what is different about their methods 2 A family of six is going to the fair They have a coupon for 1 50 off each ticket If they pay 46 50 for all their tickets how much does a ticket cost without the coupon Write an equation to find the ticket cost without a coupon

1 Consider the function f x x 4x 8 a 5 pts Use the limit definition of derivative to find f x You must show all your work

Given the points A 2 0 B 7 13 C 1 6 D 4 5 E 2 2 and F 3 2 4 2 find the position vector equal to the following vector a AB C ET d cb b AC 2 ABD Type exact answers using radicals as needed b AC Type exact answers using radicals as needed C EF Type exact answers using radicals as needed d co Type exact answers using radicals as needed

Problem 1 Solve each logarithmic or exponential equation a e3t 11e7 t 0 b log5 2 19 logs x 5 1 c 2x 2x 23

Calculate the work done in the following situation A constant force F 3 5 1 in newtons moves an object from 0 0 0 to 2 4 8 Distance is measured in meters Simplif

Find two vectors parallel to v with three times the magnitude of v v 9 3 Select the correct two vectors below DA 9 3 3 10 3 10 B 9 3 C 9 3 10 3 3 10 3 10 D 27 9 E 9 27 F 27 9

adc m the en 3 When making their fruit juice Meghan s Deli mixes 3 parts grapefruit juice with 2 parts apple juice If Meghan uses 12 cups of apple juice how much juice will she make

y 1 List all steps of differentiation the functions 4 2x 5 4 x 1 4 and y 2x 5

X y 20 99 Below answer parts a through f 17 15 119 117 Choose the correct graph below O A 150 00 14 129 10 139 O B 30 150 90 G d Use a graphing utility to find the line of best fit y 3 8613 x 179 292 Type integers or decimals rounded to four decimal places as needed e What is the correlation coefficient r r Type an integer or decimal rounded to three decimal places as needed C 30 150 OD

1 Determine the value of k for which f x 4x kx 6 has a horizontal tangent at x 2 3

1 Determine the derivative of each of the following functions Leave your answers in unsimplified form a y 3x5 7x4 b h t 5t 2 4t 3 1 c g x 2t 3 3t2 2t 1 2 3 3

8 The amount of pollution in a certain lake is P t 1 3 where t is measured in years and P is measured in parts per million ppm At what rate is the amount of pollution changing after 16 years

2 What are the coordinates of the point on the graph of f x x 1 x 2 at which the tangent is parallel to the line with equation 3x y 1 0 3

2 Use the first principles formula to find the derivative of y x 6

1 What is the slope of the normal to y x 2 x 2 at 2 0