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Question

If f is continuous function and F(x)=x0((2t+3)2tf(u)du)dt, then the value of F′′(2)f(2)


A
3
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B
5
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C
7
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D
9
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Solution

The correct option is C 7
F(x)=x0((2t+3)2tf(u)du)dt
Differentiating both sides w.r.t. x, then 
F(x)=(2x+3).2xf(u)du
Again differentiating both sides w.r.t. x, then 
F′′(x)=(2x+3).(0f(x))+2xf(u)du×2F′′(2)=7f(2)+0F′′(2)f(2)=7

Mathematics

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