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
$(1983,1 M)$
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Answer:
Correct Answer: 28. $(a, b, c, d)$
Solution:
- $y=a \log x+b x^{2}+x$ has extremum at $x=-1$ and $x=2$.
$\therefore \quad \frac{d y}{d x}=0$, at $x=-1$
$$ \begin{aligned} & \text { and } \quad x=2 \Rightarrow \frac{a}{x}+2 b x+1=0 \text {, at } x=-1 \\ & \text { and } \quad x=2 \\ & \therefore \quad-a-2 b+1=0 \\ & \text { and } \quad \frac{a}{2}+4 b+1=0 \\ & \Rightarrow \quad a=2 \text { and } b=-\frac{1}{2} \end{aligned} $$
