If ∫f(x)cosxdx=12(f(x))2+C and f(0)=0, then f′(0)=
A
1
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B
−1
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C
0
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D
2
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Solution
The correct option is A1 If ∫f(x).cosxdx=12(f(x))2+c Differentiating w.r t x on both sides f(x)cosxdx=12.2f(x).f′(x) cos(x)=f′(x) Put x=0 ⇒f′(0)=cos0=1