Question

Let, $f\left(x\right)=x^2+bx+7$. If $f^{\prime }\left(5\right)=2f^{\prime }\left(\frac{7}{2}\right)$, then the value of $b$ is

• A. 4
• B. 3
• C. -4
• D. -3
• E. 2

Answer 1

The correct option is C -4

Given, $f\left(x\right)=x^2+bx+7$
On differentiating both sides w.r.t. $x$, we get
$f^{\prime }\left(x\right)=2x+b$
Also, $f^{\prime }\left(5\right)=2f^{\prime }\left(\frac{7}{2}\right)$
Therefore, $2\left(5\right)+b=2(2\times \frac{7}{2}+b)$
$\Rightarrow 10+b=14+2b$
$\Rightarrow b=-4$