A continuous and differentiable function $y=f(x)$ is such that it's graph cuts line $y=m x+c$ at $n$ distinct points. Then the minimum number of points at which $f^{\prime \prime}(x)=0$ is

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Analyzing +4 | -1

A continuous and differentiable function

y=f(x)

is such that it's graph cuts line

y=m x+c

n

distinct points. Then the minimum number of points at which

f^{\prime \prime}(x)=0

View answer and explanation

Correct option: C

{n}-2

Option C (

{n}-2

) is correct because by applying LMVT and Rolle's theorem, we can deduce that there are at least n-2 points where the second derivative is zero.

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[x]

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\frac{{dy}}{{dx}}

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