Problem Statement

{20,30,40}
{50,60}
round(1.1 + 0.108*40,2)
round(1.1 + 0.108*50,2)

The stopping distance for an automobile is F(s) = 1.1s + 0.054s2 ft, where s is the speed in mph. Use the Linear Approximation to estimate the change in stopping distance per additional mph when s = 40 and when s = 50.

 
Step 1

Question Sequence

Question 1

If the function F is differentiable at s = a and Δs is small, then the Linear Approximation of ΔF is

ΔF ≈ ,

where Δs represents the change in s.

Correct.
Incorrect.

Question 2

To use Linear Approximation to estimate the change in stopping distance per additional mph, ΔF, first we need to find F'(40) and F'(50).

Find F'(40)Δs and F'(50)Δs, respectively.

F(s) = 1.1s + 0.054s2

F'(s) = 1.1 + 0.108s ft/mph

F'(40) = ft/mph

F'(50) = ft/mph

(Round your answers to two decimal places.)

Correct.
Incorrect.

 
Step 2

Question Sequence

Question 3

To estimate the change in stopping distance per additional mph, use Δs = mph.

Correct.
Incorrect.

Question 4

Compute F'(40)Δs and F'(50)Δs, respectively.

F'(40)Δs =

F'(50)Δs =

(Round your answers to two decimal places.)

Correct.
Incorrect.

 
Step 3

Use the Linear Approximation to estimate ΔF at s = 40 mph and at s = 50 mph.

Question Sequence

Question 5

At s = 40 mph, the change in stopping distance per additional mph is

ΔF ≈ ft.

(Round your answer to two decimal places.)

Correct.
Incorrect.

Question 6

At s = 50 mph, the change in stopping distance per additional mph is

ΔF ≈ ft.

(Round your answer to two decimal places.)

Correct.
Incorrect.