Question

given that f(100) = 150, f'(100) = -3, find f'(105.5)

Answer 1

are you sure it isn't f(105.5)? this is like a linear approximation problem

Answer 2

I was wondering the same thing.

You want to get the new f from the adding the slope times the small change in the independent variable to the original f.

f(b) = f(a) + (df/dx)(b-a)

usually need (b-a) small.

Answer 3

the formula above is the linear approximation formula, so i'm guessing it is indeed approximating f(105.5)

L(105.5) = f(100) + f'(100) (105.5 - 100)
= 150 - 3(5.5)
= 133.5