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  • A function is defined over an open interval <img alt="\mathrm{

A function \mathrm{y=5 x^2+10 x} is defined over an open interval \mathrm{x=(1,2)}. At least at one point in this interval, \mathrm{\frac{d y}{d x}} is exactly

Option: 1

20


Option: 2

25


Option: 3

30


Option: 4

35


Answers (1)

best_answer

                  \mathrm{y=5 x^2+10 x, x \in(1,2)}

                 \mathrm{\frac{d y}{d x}=10 x+10}

Given that, \mathrm{1<x<2}

\mathrm{\Rightarrow}              \mathrm{\begin{aligned} & 10<10 x<20 \\ & 20<10 x+10<30 \end{aligned}}

\mathrm{\therefore \frac{\mathrm{dy}}{\mathrm{dx}}}  is exactly 25 at atleast one point in the open interval \mathrm{(1,2)}.

Posted by

Ritika Kankaria

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