Differentiation Questions and Answers

Given the points 2 4 and 1 10 find the slope

1 Which is the correct formula for finding the derivative of the product of two functions O fg f g O fg fg gf fg f g 2 Use the correct formula above to find the derivative of the function f x x e

Question 2 1 point 4 Listen In rectangle ABCD X and Y are midpoints of AB and AD respectively If a AX and b AY then DB is equal to AX O a 26 2a b 2a 2b c 2a 26

Listen ABCD is a square Express AC BC as a single vector O a O b b CD c DA d AD DC

Consider the velocity function for an object moving along a line shown in the figure a Describe the motion of the object over the interval 0 13 b Use geometry to find the displacement of the object between t 0 and t 2 c Use geometry to find the displacement of the object between t 2 and t 10 d Assuming that the velocity remains 10 m s for t 10 what is the displacement function between t 0 and any time t 10 a Describe the motion of the object over the interval 0 13 The object is slowing down speeding up ww on 6 10 and b The displacement of the object between t 0 and t 2 is Simplify your answer Velocity m s m VA 40 30 20 on the interval 0 1 moving at a constant rate on 1 6 moving at a constant rate on 10 13 104 0 0 2 4 6 8 10 12 14 1 Time s

Use the chain rule to find the derivative of f x 5 6x 9x6 16 You do not need to expand out your answer f x

Determine two coterminal angles in degree measure one positive and one negative for each angle There are many corre answers Enter your answers as a comma separated list a b Q 0 118 0 398

Convert each radian measure to degree measure Do not use a calculator 3 a 2 b 5T 6

Find the are length function for the curve t t sinxt cosat starting from the point 0 0 1 in the direction of increasing t

I Fon the function f x y 2x 2y 2xy x y 151 classity the critical points 1 0 and T t 7 t JR t d 45 ds K 7 IT HOT t 17 4 PHI TH NH F X F t 7 1

8 Find the function f x y 2x 2y 2xy x y classify the critical points 1 0 and 3 3 12 3

7 Fon R R t u where t t w x y z and u u w x y z Use the Chain rule to write out the partial derivatives of R with respect to w x y and 2

Fon the curve R t Sinzt t cosat Find ti Unit tangent vector

3 Let f be a differentiable function of z If y f a define the differential of y dy at 2 mi

4 Fill in each blank with the correct derivative a k 0 b cf x cf 1 d f x g x x 9 dfg c f x g x gfa f x gx2 f 8 g x fg h d f 2 dr i cos x dr iii d i sin x dr iv v sin z COS X ii cos 7 d da sinx tan x x 1 cot 7 sec x Tdx 1 x 1 x x 1 i tanz dr k 1 m n o vii d d viii cot z dr sec x csc x In z In x Sec x csc x sec x ton x cot x csc x p log z 9 ex x 6 b In b 3 vi esc 2 x x 1 4 cosh x 1 In b d sinhr dr cosh x d ix tanhz sech x r dr sin h x d x sech Sech x tanh x z dr

9 The area of an ellipse is given by the formula A ab where a is the semi major axis and b is the semi minor axis Imagine that a garden is to be constructed such the semi minor axis is to be 1 4 of the semi major axis Given that the maximum percent error when measuring a is 2 use a differential to estimate the maximum percent error when calculating the area

Evaluate the following limits If needed enter oo for and o0 for 00 4 4z 9 3x a lim 818 4 4x 9 31 Question Help Video b lim 8118 x 0 66666666666667

3 X 2 1 3 2 1 For the above rational function f x 1 2 3 15 2 5x2 3 identify the interval on which f is concave dow

A farmer finds that if she plants 100 trees per acre each tree will yield 40 bushels of fruit She estimates that for each additional tree planted per acre the yield of each tree will decrease by 4 bushels How many trees should she plant per acre to maximize her harvest trees Give your answer rounded to the nearest whole number

Write the sum using sigma notation 8 11 14 17 47 B where AB A B A n 1

If 1100 square centimeters of material is available to make a box with a square base and an open top find the largest possible volume of the box Volume cubic centimeters

A graph of y f z is shown In the same coordinate system sketch a graph of the derivative function y f z over the interval 4 4 44 3 2 1 34 2 1 3 N 3 2 4 Clear All Draw Line Segment 3

Let y 3x Find the change in y Ay when I 1 and Az Find the differential dy when I 1 and dr Question Help Video 0 4 0 4 2 1

Find the maximum rate of change of f x y ln x y2 at the point 3 5 and the direction in which it occurs Maximum rate of change Direction unit vector in which it occurs

1 point If z tan of u and u dz du dz and x u and y find the following partial derivatives using the chain rule Enter your answers as functio

The functions f x and g x are graphed below 5 4 3 2 5 3 2 1 2 3 4 5 1 2 3 4 5 5 4 3 2 Determine f 2 4 Determine g 2 1 Determine f g 2 Determine f 2 2 Determine g 2 1 Determine f g 2 Determine f 4 Determine g 4 Determine g f 4 Determine f 1 Determine g 1 3 3 5 7 2 3 45 5 2 3 4 5

Rylan enjoys adding her own toppings to a frozen pizza She bakes her frozen pizza on a pizza stone that is 12 inches in diameter and inch thick What is the surface area of the pizza stone Round to the nearest hundredth

1 point Use the chain rule to find First the pieces dr End result in terms of just 1 de where z x y xy x 4 1 y 5 f

Listen To three decimal places the slope of the tangent to the curve f x log10 1 is a 0 434 b 0 251 c 1 000 d 0 868 Question 2 1 point Saved Listen In comparison to f x a the function g x 4a a Is stretched vertically by a factor of 4 right

10 1 Points SCALCET8 5 1 015 V approx L lower estimate V L upper estimate

a The image of the school bus is 5 cm long The scale is 1 300 K 5 cm length of each object Use scale diagram measurement actual measurement The actual length is b The diagram of the mosquito is 32 mm long The scale is 1 0 5 216 32 mm The actual length is c The scale diagram of a skateboard has a scale of 1 14 What is the actual length of the skateboard The actual length of the chinook salmon is The actual length of the skateboard is d The scale for the diagram of the chinook salmon is 1 9 2 Calculate the actual length of the salmon to cm 5 5 cm 5 cm

Find the derivative of the vector function r t r t ln 12 i 5 1j 4e k 9

What is the value of log 343 0 1 PRE 3

Which statement is true O y log10X is not a logarithmic function because the base is greater than 0 O y log 3x is not a logarithmic function because the base is a square root O y log x is not a logarithmic function because the base is equal to 1 O y log2x is not a logarithmic function because the base is a fraction

What is the range of Y log Oall real numbers less than 0 O all real numbers greater than 0 all real numbers not equal to 0 all real numbers

Textbook Approximate the area under the curve graphed below from x 2 to x 7 using a Left Endpoint approximation with 5 subdivisions 3 2 1 1 2 3 4 5 Videos 6

Evaluate the integral below by 5 1 1 0 V A1 f x dx y f x 3 interpreting it in terms of areas in the figure The areas of the labeled regions are A1 7 A2 3 A3 1 and A4 1 A2 5 A3 7 A4 figure is NOT to scale 10

t the vector po f Y x y rank when x 0 y 0 Calculate the Jacobian matrix and find 4 Marks

Textbook 26 S f x dx where a videos 19 S f x dz S 10 f x dz and b

Let g x x 1 The absolute minimum value of g over the closed interval 2 x 3 occurs Choose 1 answer A 0 B 2 7 3

Let f x y be a positive function Consider the following double integrals 1 LL 0 a b C 1 L S 1 0 0 1 3 x f x y dydr f x y dydx f x y dydr Rank the integrals from smallest to largest value In each box below enter the letter a b or c

Textbook Videos dr Let A be the area of a circle with radius r If dt 5 find dA dt when r 1

Which equation is equivalent to 24x8 3 24x22x 3 24x22x 6 24x23x 3 24x23x 9

Next question Get a similar question You can retry this qu Let f z 5 4 f z has one critical value at A For z A f z is Decreasing Forz A f x is Decreasing 0

Consider the function f z 6z 2z For this function there are four important intervals o A A B B C and C oo where A and C are the critical numbers and the function is not defined at B Find A and B and C For each of the following intervals tell whether f x is increasing type in INC or decreasing type in DEC 0 A A B B C C 00

What is the measure of Za Angles are not necessarily drawn to scale A 33 J F B 46 I G H

P given by P t 20 10te t 3 9 as a model for the temperature of the water in the pond at time 9 t where t is measured in days and P t is measured in degrees Celsius Find P 12 Using appropriate units explain the meaning of your answer in the context

The radius of a sphere is decreasing at a constant rate of 6 feet per second At the instant when the volume of the sphere is 163 cubic feet what is the rate of change of the volume The volume of a sphere can be found with the equation V places Round your answer to three decimal Answer

Q3 If y x cos 2 ln x is a solution of Ax y Bx y m Cxy n Dxy 0 where A B C D m ne NU 0 Find all possible values of A B C D m and n

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