If f(x)=x^3+6x+7, find (f^-1)'(7)

Answer 1

Given the function f(x)=x^3+6x+7

First, you'll have to determine what value of x will give us 7.

7=x^3+6x+7

x^3+6x=0

x=0

Then you find the derivative of the function using power rule:

f'(x)=3x^2+6

and now plug in x=0

f'(0)=0+6=6

Finally use the inverse function derivative formula: d/dx(f^-1(x))= 1/f'(f^-1(x))

1/f'(f^-1(7))= 1/f'(0)= 1/6

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