Mathematics - Application of Derivative Question with Solution | TestHub

Let ${\mathrm{f}}^{\prime }(1)=\mathrm{a},{\mathrm{f}}^{\prime \prime }(2)=\mathrm{b},{\mathrm{f}}^{\prime \prime \prime }(3)=\mathrm{c}$

so ${\mathrm{f}}^{\prime }(\mathrm{x})=3{\mathrm{x}}^2+2\mathrm{ax}+\mathrm{b},{\mathrm{f}}^{\prime \prime }(\mathrm{x})=6\mathrm{x}+2\mathrm{a}$

$\mathrm{a}=3+2\mathrm{a}+\mathrm{b}$

$\mathrm{b}=12+2\mathrm{a}$ and $\mathrm{c}=6$.

$\Rightarrow \mathrm{a}=-5,\mathrm{b}=2$ and $\mathrm{c}=6$. so $\mathrm{a}+\mathrm{b}+\mathrm{c}=3$