Application of Derivatives 4 Question 27

####28. If $y=a \log x+b x^{2}+x$ has its extremum values at $x=-1$ and $x=2$, then

(a) $a=2, b=-1$

(b) $a=2, b=-\frac{1}{2}$

(c) $a=-2, b=\frac{1}{2}$

(d) None of the above

$(1983,1 \mathrm{M})$

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Answer:

Correct Answer: 28. $(a, b, c, d)$

Solution:

  1. $y=a \log x+b x^{2}+x$ has extremum at $x=-1$ and $x=2$.

$\therefore \quad \frac{d y}{d x}=0$, at $x=-1$

$ \begin{aligned} & \text { and } \quad x=2 \Rightarrow \frac{a}{x}+2 b x+1=0 \text {, at } x=-1 \\ & \text { and } \quad x=2 \\ & \therefore \quad-a-2 b+1=0 \\ & \text { and } \quad \frac{a}{2}+4 b+1=0 \\ & \Rightarrow \quad a=2 \text { and } b=-\frac{1}{2} \end{aligned} $



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