JEE MATHEMATICS MCQ: INCREASING & DECREASING

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Analyzing +4 | -1

Let

f

be a twice differentiable function for all real

x

f(1)=1, f(2)=4

and

f(3)=9

. Then which one of the following statements is definitely true?

View answer and explanation

Correct option: D

f^{\prime \prime}(x)

attains the value 2 for some

x \in(1,3)

Option D (

f^{\prime \prime}(x)

attains the value 2 for some

x \in(1,3)

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

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

, we can show that there exists a point in (1,3) where the second derivative of f(x) is 2.

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