If f(x) = x^3 + 7x + 2 , find (f^-1)’(1)

Answer 1

As I understand the question, you are looking for 1[(f'(-1)], the inverse of the derivative of f at x=1.

Step 1: we first take the derivative of f(x) = x³+7x+2.

The derivative will be f'(x) = 3x²+7. (with derivatives, we take the exponent and multiply it by the number in front of the variable)

Step 2: then, we will take the inverse of this function as we are looking for the inverse of the derivative at x=1.

The inverse will be 1/f'(x) = 1/(3x²+7)

Step 3: we now plug in one as we are looking for the inverse of the derivative at x=1.

we get: 1/f'(1) = 1/[3(1)²+7] = 1/(3+7) = 1/10.