Question

State the following statement is True or False

$f\left(x\right)=2x^3-21x^2+36x-30$ is maximum at $x=1$.

• A. True
• B. False

Answer 1

The correct option is A True

$f\left(x\right)=2x^3-21x^2+36x-30$

$f^{\prime }\left(x\right)=\frac{d\left(f\right(x\left)\right)}{dx}=2\times 3x^2-21\times 2x+36=6(x^2-7x+6)$

$f^{\prime \prime }\left(x\right)=6(2x-7)$

Equating $f^{\prime }\left(x\right)$ to zero, we have $x^2-7x+6=0$

$\Rightarrow (x-1)(x-6)=0$ or $x=1,6$

$f^{\prime \prime }\left(1\right)=6(2-7)<0$

$\Rightarrow f\left(x\right)$ has a maximum at $x=1$