Linear Approximation

Question

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 = 25.

Use the Linear Approximation to estimate the change in stopping distance per additional mph when s = 65.

Answer 1

if F(s) = 1.1s + .054s² then df = 1.1 + .108s ds

at s = 25 dF = 1.1 + .108(25)(1) = 3.8 ft

for s = 65 dF = 1.1 + .108(65)(1) = 8.12 ft