To determine
To find: (f-1)'(5)
Answer
Answer: (f-1)'(5)=1/6
Explanation
Given: fx=3x3+4x2+6x+5.
The derivative of f is f'x=9x2+8x+6.
Since f'x>0, f is an increasing function. Therefore, f is a one to one function. Also f0=5 ⇒ f-15=0 and f'0=6.
Conclusion: By Theorem 7,
(f-1)'(5)=1/f'(f-15)=1/f'(0)=1/6.