If $y=a \log x+b x^2+x$ has its extreme value at $x=-1$ and $x=2$, then the value of $\mathrm{a}+\mathrm{b}$ is

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Aicharya · Accepted Answer

$\begin{aligned} & y=a \log x+b x^2+x \ & \frac{d y}{d x}=\frac{a}{x}+2 b x+1 \ & \left(\frac{d y}{d x}ight)_{x=-1}=-a-2 b+1=0 \ & \Rightarrow a+2 b=1...(i) \end{aligned}$ and $\left(\frac{d y}{d x}ight)_{x=2}=\frac{a}{2}+4 b+1=0$ $\begin{aligned} & \Rightarrow a+8 b+2=0 \ & \Rightarrow a+8 b=-2...(ii) \end{aligned}$ Solving (i), (ii) we get $\begin{array}{cc} & b=\frac{-1}{2} 	ext { and } a=2 \ 	herefore \quad & a+b=2+\left(\frac{-1}{2}ight)=\frac{3}{2} \end{array}$

If $y=a \log x+b x^2+x$ has its extreme value at $x=-1$ and $x=2$, then the value of $\mathrm{a}+\mathrm{b}$…

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