Question

The number of points of inflection for $f\left(x\right)=\frac{x^4}{12}-\frac{x^3}{2}+x^2+7x+8$ is

• A. $0$
• B. $1$
• C. $2$
• D. more than $2$

Answer 1

The correct option is C $2$

$f\left(x\right)=\frac{x^4}{12}-\frac{x^3}{2}+x^2+7x+8$
$\Rightarrow f^{\prime }\left(x\right)=\frac{x^3}{3}-\frac{3x^2}{2}+2x+7\Rightarrow f^{\prime \prime }\left(x\right)=x^2-3x+2=(x-1)(x-2)$
Sign scheme for $f^{\prime \prime }\left(x\right):$

$f^{\prime \prime }\left(x\right)$ changes its sign about $x=1$ and $x=2.$
So, $x=1,2$ are points of inflection.