Question

Let $f(x)=x^{3}+3 x+2$ and $x=c$ be a point such that $f'(c) \neq \frac{f(b)-f(a)}{b-a}$ for any two values of $a, b \in R $, then number of such point is ___.

Answer 1

For such points $x=c, f''(c)=0$
$\therefore $ there is one point only