Question

Let $f\left(x\right)=x^3-x^2+12x-3$ then at $x=2$, $f\left(x\right)$ has?

• A. A maximum
• B. A minimum
• C. Both a maximum and a minimum
• D. Neither a maximum nor a minimum

Answer 1

The correct option is A A maximum

Given:

$f\left(x\right)=x^3-x^2+12x-3$

Solution:

$f\left(x\right)=x^3-x^2+12x-3$

$\Rightarrow f^{\prime }\left(x\right)=3x^2-2x+12$

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

at x=2

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

$\Rightarrow f^{\prime \prime }\left(2\right)=12-2$

$\Rightarrow f^{\prime \prime }\left(2\right)=10>0$

we get,

$f^{\prime \prime }\left(x\right)>0$

$\therefore$ at x=2 , f(x) is maximum.