Find (f ^(−1))'(a). f(x) = 4x3 + 4x2 + 6x + 8, a = 8

Answer 1

By inspection, we see that f(0) = 8.

So, [f^-1(8)]' = 1 / f'(0)

f(x) = 4x³ + 4x² + 6x + 8

f'(x) = 12x² + 8x + 6

f'(0) = 26

So, [f^-1(8)]' = 1 / f'(0) = 1/26