Question

find (f^(-1))'(a) for the function f and the given real number a. f(x) = 1/27(x^5 + 2x^3), a = -11

Answer 1

if f(x) = 1/27 (x^5 + 2x^3), what did you get for its inverse ?

Answer 2

actually that is way too difficult to figure out. try another approach.

what do we know about the relationship between the slopes of functions and the slopes of their inverses ?

Answer 3

you will see that they are multiplicative inverses of one another. so if you can find the slope of f(x) at a then you can just take the multiplicative inverse of it to find the slope of the inverse function at a.