First slide

Maxima and minima

Question

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

Moderate

A

$a = 2, b = - 1$
B

$a = 2, b = - 1 / 2$
C

$a = - 2, b = 1 / 2$
D

$none of these$

Solution

$We have y^{'} = a l x + 2 b x + 1 and y^{'} (- 1) = 0 and y^{'} (2) = 0$
$∴ - a - 2 b + 1 = 0$
$\begin{array}{l} and \\ a / 2 + 4 b + 1 = 0 \\ \Rightarrow a / 2 - 2 a + 2 + 1 = 0 \\ Hence a = 2 and b = - 1 / 2 \end{array}$

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