Question

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

• A. $4$
• B. $3$
• C. $-4$
• D. $-3$

Answer 1

The correct option is C

$-4$

Explanation for the correct option.

Find the value of $b$.

The derivative of the function $f\left(x\right)=x^2+bx+7$ is given as: $f\text{'}\left(x\right)=2x+b$.

Now for $f\text{'}\left(x\right)=2x+b$, the equation $f\text{'}\left(5\right)=2f\text{'}\left(\frac{7}{2}\right)$ becomes

$$\begin{gathered} 2\left(5\right)+b=2\left[2\times \frac{7}{2}+b\right] \\ \Rightarrow 10+b=14+2b \\ \Rightarrow 10-14=2b-b \\ \Rightarrow -4=b \end{gathered}$$

So the value of $b$ is $-4$.

Hence, the correct option is C.