Question

Let $f:R \rightarrow R,f\left(x\right)=x^{4}-8x^{3}+22x^{2}-24x+c.$ 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)

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