JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

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Application +4 | -1

Let

\mathrm{F(x)=f(x) g(x) h(x)}

for all real

\mathrm{x}

, where

\mathrm{f(x), g(x)}

and

\mathrm{h}(\mathrm{x})

are differentiable functions. At some point

\mathrm{x}_0, \mathrm{F}^{\prime}\left(\mathrm{x}_0\right)=21 \mathrm{F}\left(\mathrm{x}_0\right), \mathrm{f}^{\prime}\left(\mathrm{x}_0\right)=4 \mathrm{f}\left(\mathrm{x}_0\right), \mathrm{g}^{\prime}\left(\mathrm{x}_0\right)=-7 \mathrm{g}\left(\mathrm{x}_0\right)

and

\mathrm{h}^{\prime}\left(\mathrm{x}_0\right)=\operatorname{kh}\left(\mathrm{x}_0\right)

. Then the value of

\mathrm{k} / 8

View answer and explanation

Correct option: A

Option A (3) is correct because by differentiating F(x) and substituting the given conditions, the value of k/8 is found to be 3.

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