Derivatives — MATHS STD 11 Science — Question

$\text{f}(\text{x})=\lambda\text{x}^2+\mu\text{x}+12$

$\Rightarrow\text{f}'(\text{x})=\text{2x}\lambda+\mu\dots(\text{i})$

but, $\text{f}'(4)=15$

from (i)

$8\lambda+\mu=15\dots(\text{ii})$

also, $\text{f}'(\text{12})=11$

$4\lambda+\mu=11\dots(\text{iii})$

(ii)-(iii) gives

$4\lambda=4$

$\Rightarrow\lambda=1$

from (ii)

$8.1+\mu=15$

$\Rightarrow\mu=7$

Hence,

$\lambda=1$ and $\mu=7$