Let f:[a, b] \to C be continuous in [a, b], differentiable in (a, b) and f(a)=0=f(b). Then

Correct Answer is : there exists at least one point c∈(a,b) for which f′(c)=f(c)

there exists at least one point c \in(a, b) for which f^{'}(c)=f(c)

f^{'}(x)=f(x) does not hold at any point of (a, b)

at every point of (a, b), f^{'}(x) > f(x)

at every point of (a, b), f^{'}(x)

WBJEE 2022 Math Solved Paper

Question : 14 of 75

Marks: +1, -0

Let f:[a,b]→C be continuous in [a, b], differentiable in (a,b) and f(a)=0=f(b). Then

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