If `f(x)=A x^2+B x+C` is such that `f(a)=f(b)` , then write the value of `c` in Rolles theorem.

Answer

`C=frac{a+b}{2}`

Explanation

$$ f(x)=A x^{2}+B x+C $$
Differentiating w.r.t. ' `X` ',
$$
\begin{aligned}
&f^{\prime}(x)=2 A x+B \\
&f^{\prime}(c)=2 A C+B \\
...