Differentials question

Question

I'm not even sure where to start with this one, I've been trying to find dT first but I'm not sure what to do after.

The total stopping distance T of a vehicle is shown below, where T is in feet and x is the speed in miles per hour.

T = 2.5x + 0.5x²

Approximate the change and percent change in total stopping distance as speed changes from x = 35 to x = 36 miles per hour. (Round your answers to one decimal place.)

It asks for A) dT = __ and B) dT/T= __

Answer 1

Here's the general method; you should be able to apply it to this specific function.

Since T = f(x), we have dT = f'(x)dx, where dT is the approximate change in T when x changes by the amount dx. In this case x changes from 35 to 36, thus dx = 1 and dT = f'(35)*(1).

dT/T is usually called the relative change; you'll compute this and then convert it to a percentage. You already have dT computed above; use the value of T at the original value of x = 35 in this part.