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# Solution for The Function Y = a Log X+Bx2 + X Has Extreme Values at X=1 and X=2. Find a and B ? - CBSE (Commerce) Class 12 - Mathematics

#### Question

The function y = a log x+bx2 + x has extreme values at x=1 and x=2. Find a and b ?

#### Solution

$\text { Given }: f\left( x \right) = y = a \log x + b x^2 + x$

$\Rightarrow f'\left( x \right) = \frac{a}{x} + 2bx + 1$

$\text { Since }, f'\left( x \right) \text { has extreme values at x = 1 and x = 2,} f'\left( 1 \right) = 0 .$

$\Rightarrow \frac{a}{1} + 2b\left( 1 \right) + 1 = 0$

$\Rightarrow a = - 1 - 2b . . . \left( 1 \right)$

$f'\left( 2 \right) = 0$

$\Rightarrow \frac{a}{2} + 2b\left( 2 \right) + 1 = 0$

$\Rightarrow a + 8b = - 2$

$\Rightarrow a = - 2 - 8b . . . \left( 2 \right)$

$\text { From eqs } . \left( 1 \right) \text { and } \left( 2 \right), \text { we get }$

$- 2 - 8b = - 1 - 2b$

$\Rightarrow 6b = - 1$

$\Rightarrow b = \frac{- 1}{6}$

$\text { Substituting b } = \frac{- 1}{6} \text { in eq } . \left( 1 \right), \text{we get }$

$a = - 1 + \frac{1}{3} = \frac{- 2}{3}$

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Solution The Function Y = a Log X+Bx2 + X Has Extreme Values at X=1 and X=2. Find a and B ? Concept: Graph of Maxima and Minima.
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