JEE MATHEMATICS MCQ: MEAN VALUES THEOREM

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Application +4 | -1

f(x)=(1-x)^{3 / 2}

satisfies the relation

f(x)=f(0)+x f^{\prime}(0)+\frac{x^2}{2} f^{\prime \prime}(\theta x)

then as

x \rightarrow 1

, the value of

\theta

View answer and explanation

Correct option: D

\frac{9}{25}

Option D (9/25) is correct because it is the value of θ that satisfies the given relation as x approaches 1, found by using Taylor's theorem.

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