Question

Find (f^-1)'(7) without finding the inverse function where f(x) = 5 – 2x^3.

Answer 1

Explanation:

the derivative of an inverse function is

1/f'(f^-1(x))

f'(x) = -6x²

f^-1(7) is solving the original function equation for x under the knowledge that y = 7

7 = 5 - 2x³

2 = -2x³

-1 = x³

=>

x = -1

f'(-1) = -6×(-1)² = -6×1 = -6

so,

(f^-1)'(7) = -1/6