Question

Let f(x) = log x + x³ and let g(x) be the inverse of f(x), then |64g"(1)| is equal to ______.

Options

• 5.00

• 6.00

• 7.00

• 8.00

Answer 1

Let f(x) = log x + x³ and let g(x) be the inverse of f(x), then |64g"(1)| is equal to 5.00.

Explanation:

g'f(x) = `1/(f^'(x))`

⇒ g"(f(x)).f'(x) = `-1/((f^'(x))^2).f^('')(x)`

⇒ g"(logx + x³) = `(-(6x - 1/x^2))/((1/x + 3x^2))`

Put x = 1

⇒ g"(1) = `-5/64`

⇒ |64g"(1)| = 5