Q. Given that the function $h(x)=x^3+2 x+1$ for $x \in R$ has an inverse $h^{-1}$ on $R$, then the value of $\left( h ^{-1}\right)^{\prime}(1)$ is
Continuity and Differentiability
Solution:
$ \therefore\left( h ^{-1}\right)^{\prime}=(1)=\frac{1}{ h ^{\prime}(0)}=\frac{1}{2} $
$\text { As } h ( x )= x ^3+2 x +1 $
$\Rightarrow h^{\prime}(x)=3 x^2+2$
