Question

The value of c is Rolle's theorem when $f\left(x\right)=2x^3-5x^2-4x+3,xϵ[1/2,3]$ is

• A. $2$
• B. $-\frac{1}{3}$
• C. $-2$
• D. $\frac{2}{3}$

Answer 1

The correct option is A $2$

$f\left(x\right)=2x^3-5x^2-4x+3,xϵ[1/2,3]$
$f^{\prime }\left(x\right)=2(3x^2-5x-2)$
Since, Rolle's theorem holds for $c\in (2,3)$ such that
$f^{\prime }\left(c\right)=0$
$\Rightarrow 3c^2-5c-2=0$ .....(i)
Since, value of c given in option B and D does not lie in (2,3),
Option A only satisfies equation (i),
Hence, $c=2$