Question

Let $f:R\to R,f\left(x\right)=x^4-8x^3+22x^2-24x+c.$ If sum of all local extremum values of $f\left(x\right)$ is $1,$ then $c$ is equal to

• A. $8$
• B. $9$
• C. $10$
• D. $11$

Answer 1

Answer: (B)

$f^{{}^{\prime }}\left(x\right)=4\left(x^3-6x^2+11x-6\right)$
$=4\left(x-1\right)\left(x-2\right)\left(x-3\right)$
Hence, $x=1,2,3$ are points of extrema
So, $f\left(1\right)+f\left(2\right)+f\left(3\right)=1$
$\left(c-9\right)+\left(c-8\right)+\left(c-9\right)=1\Rightarrow c=9$