Mathematics - Application of Derivative Question with Solution | TestHub

${\mathrm{f}}^{\prime }(0)=0$ and ${\mathrm{f}}^{\prime \prime }(0)>0$ $\mathrm{y}=\mathrm{f}(\mathrm{x})+\mathrm{ax}+\mathrm{b}$ has a relative minimum at $\mathrm{x}=0$. Then $\begin{array}{rlrl}& \frac{dy}{dx}=0\text{ at }x=0& f^{\prime }(x)+a=0\Rightarrow a=0& f^{\prime \prime }(x)>0\Rightarrow f^{\prime \prime }(0)>0\end{array}$

Hence y has relative minimum at $\mathrm{x}=0$ if $\mathrm{a}=0$ and $\mathrm{b}\in \mathrm{R}$.