Question

If for $f\left(x\right)=\lambda x^2+\mu x+12$, $f^{\prime }\left(4\right)=15$ and $f^{\prime }\left(2\right)=11$, then find $\lambda$ and $\mu$.

• A. $2$ and $7$
• B. $1$ and $7$
• C. $7$ and $7$
• D. None of these

Answer 1

The correct option is B $1$ and $7$

$f\left(x\right)=\lambda x^2+\mu x+12$

$f^1\left(x\right)=2\lambda x+\mu$

$f1\left(4\right)=15$

$\Rightarrow \left(4\right)+\mu =15$

$8\lambda +\mu =15$ ........ $\left(1\right)$

$f^1\left(2\right)=11$

$\Rightarrow 2\lambda \left(2\right)+\mu =11$

$4\lambda +\mu =11$ ........ $\left(2\right)$

$\left(1\right).....\left(2\right)$

$\Rightarrow 4\lambda =4\Rightarrow \lambda =1$

$8\left(1\right)+\mu =15\Rightarrow \mu =7$

$\therefore \lambda =1\&\mu =7$