Question

If function $f\left(x\right)=x^3-62x^2+ax+9$ has local maxima at $x=1$, then find the value of a

• A. $121$
• B. $144$
• C. $81$
• D. $169$

Answer 1

The correct option is A $121$

$f\left(x\right)=x^3-62x^2+ax+9$
$f^{\prime }\left(x\right)=3x^2-124x+a$
Given at $x=1,f\left(x\right)$ attains its local maxima,
$\Rightarrow f^{\prime }\left(1\right)=0$

$\Rightarrow 3-124+a=0$

$\Rightarrow a=121$