Chapter 1.

1.1 Problem Statement

{20,30,40}

{50,60}

round(1.1 + 0.108*$s1,2)

round(1.1 + 0.108*$s2,2)

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 = $s1 and when s = $s2.

1.2 Step 1

Question Sequence

Question 1.1

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

ΔF ≈ B3lCeNir/NfP3RILH6ECIWW8LigpGa3llhPc8T9XZeg=,

where Δs represents the change in s.

Correct.

Incorrect.

Question 1.2

To use Linear Approximation to estimate the change in stopping distance per additional mph, ΔF, first we need to find F'($s1) and F'($s2).

Find F'($s1)Δs and F'($s2)Δs, respectively.

F(s) = 1.1s + 0.054s²

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

F'($s1) = UFPfACDOxzX9rlDg ft/mph

F'($s2) = 2Og4UEB2nw1H7dPo ft/mph

(Round your answers to two decimal places.)

Correct.

Incorrect.

1.3 Step 2

Question Sequence

Question 1.3

To estimate the change in stopping distance per additional mph, use Δs = 0VV1JcqyBrI= mph.

Correct.

Incorrect.

Question 1.4

Compute F'($s1)Δs and F'($s2)Δs, respectively.

F'($s1)Δs = UFPfACDOxzX9rlDg

F'($s2)Δs = 2Og4UEB2nw1H7dPo

(Round your answers to two decimal places.)

Correct.

Incorrect.

1.4 Step 3

Use the Linear Approximation to estimate ΔF at s = $s1 mph and at s = $s2 mph.

Question Sequence

Question 1.5

At s = $s1 mph, the change in stopping distance per additional mph is

ΔF ≈ UFPfACDOxzX9rlDg ft.

(Round your answer to two decimal places.)

Correct.

Incorrect.

Question 1.6

At s = $s2 mph, the change in stopping distance per additional mph is

ΔF ≈ 2Og4UEB2nw1H7dPo ft.

(Round your answer to two decimal places.)

Correct.

Incorrect.