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

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For what values of x is the rate of increase of

x^{3} - 5 x^{2} + 5 x + 8

is twice rate of increase of x ?

Options:

A . −3,−13

B . −3,13

C . 3,−13

D . 3,13

Answer: Option D
:
D
Let

y = x^{3} - 5 x^{2} + 5 x + 8

. Then,

\frac{d y}{d x} = (3 x^{2} - 10 x + 5) \frac{d x}{d t} W h e n \frac{d y}{d t} = 2 \frac{d x}{d t}, w e h a v e (3 x^{2} - 10 x + 5) \frac{d x}{d t} = 2 \frac{d x}{d t} \Rightarrow 3 x^{2} - 10 x + 3 = 0 \Rightarrow (3 x - 1) (x - 3) = 0 \Rightarrow x = 3, \frac{1}{3}

.
Hence (d) is the correct answer.

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