To determine
To find:f-1'2
Answer
f-1'2=13
Explanation
Given:fx=x3+3sinx+2cosx.
Concept: By Theorem 7,f-1'a=1f'f-1a. Therefore,f-1'2=1f'f-12.
f'x=3x2+3cosx-2sinx.
f(x)=3x2+3sinx+2cosxf′(x)=3x2+3cosx−2sinxf′(0)=0+3−0f′(0)=3
Also,f0=2f-12=0.
Conclusion: So,f-1'2=1f'f-12=1f'0=13.