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# Solution for For What Values of X is the Rate of Increase of X3 − 5x2 + 5x + 8 is Twice the Rate of Increase of X ? (A) − 3 , − 1 3 - CBSE (Science) Class 12 - Mathematics

ConceptRate of Change of Bodies Or Quantities

#### Question

For what values of x is the rate of increase of x3 − 5x2 + 5x + 8 is twice the rate of increase of x ?

(a) $- 3, - \frac{1}{3}$

(b) $- 3, \frac{1}{3}$

(c) $3, - \frac{1}{3}$

(d) $3, \frac{1}{3}$

#### Solution

(d) $3, \frac{1}{3}$

$\text { Let }y = x^3 - 5 x^2 + 5x + 8$
$\Rightarrow \frac{dy}{dt} = \left( 3 x^2 - 10x + 5 \right)\frac{dx}{dt}$
$\text { According to the question },$
$\Rightarrow 2\frac{dx}{dt} = \left( 3 x^2 - 10x + 5 \right)\frac{dx}{dt}$
$\Rightarrow 3 x^2 - 10x + 5 = 2$
$\Rightarrow 3 x^2 - 10x + 3 = 0$
$\Rightarrow 3 x^2 - 9x - x + 3 = 0$
$\Rightarrow 3x\left( x - 3 \right) - 1\left( x - 3 \right) = 0$
$\Rightarrow \left( x - 3 \right) = 0 \ or \ \left( 3x - 1 \right) = 0$
$\Rightarrow x = 3 \ \text {or} \ x = \frac{1}{3}$

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Solution for question: For What Values of X is the Rate of Increase of X3 − 5x2 + 5x + 8 is Twice the Rate of Increase of X ? (A) − 3 , − 1 3 concept: Rate of Change of Bodies Or Quantities. For the courses CBSE (Science), PUC Karnataka Science, CBSE (Arts), CBSE (Commerce)
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