Question

If f is defined in $\left[\begin{array}{c}1,3\end{array}\right]$ by $f\left(x\right)=x^3+b{x}^2+ax$,such that $f\left(1\right)-f\left(3\right)=0and{f}^{\prime }\left(c\right)=0$ where $c=2+\frac{1}{\sqrt{3}}$, then (a,b)=

• A. $(-6,11)$
• B. $\left(\begin{array}{c}2-\frac{1}{\sqrt{3}},2+\frac{1}{\sqrt{3}}\end{array}\right)$
• C. $(11,-6)$
• D. $(6,11)$

Answer 1

Answer: (C)

$(11,-6)$

$f^1\left(x\right)=3x^2+2bx+a$
$f^1\left(c\right)=0$
$3c^2+2bc+a=0$
$\Rightarrow a=11,b=-6$