JEE MATHEMATICS MCQ: MEAN VALUES THEOREM

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Application +4 | -1

f(x)

and

g(x)

are differentiable functions in

[0,1]

such that

f(0)=2, f(1)=6, g(0)=0, g(1)=

2 , then there exists

0 < \mathrm{c} < 1

such that

View answer and explanation

Correct option: C

f^{\prime}(c)=2 g^{\prime}(c)

Option C (

f^{\prime}(c)=2 g^{\prime}(c)

) is correct because it is derived by applying Rolle's theorem to the function

F(x) = f(x) - 2g(x)

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(a, b),

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\left|\begin{array}{ll}f^{\prime}(x) & f(a) \\ g^{\prime}(x) & g(a)\end{array}\right|=\frac{1}{a-b}\left|\begin{array}{ll}f(a) & f(b) \\ g(a) & g(b)\end{array}\right|