To determine

To find: f-1'0

Answer

Answer: f-1'0=128

Explanation

Given:fx=∫3x1+t3 dt.

Observe that f3=0. Therefore, f-10=3.

Also, by the Leibnitz’ rule,f'x=1+x3 ⇒ f'3=28.

Conclusion: By Theorem 7,f-1'0=1f'f-10=1f'3=128 .