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  4. A continuous and differentiable function y=f(x) is such that its graph cuts line y=m x+c at n distinct points. Then the minimum number of points at which f''(x)=0 is/are

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Q. A continuous and differentiable function $y=f(x)$ is such that its graph cuts line $y=m x+c$ at $n$ distinct points. Then the minimum number of points at which $f''(x)=0$ is/are

Application of Derivatives

Solution:

From LMVT, there exists at least $(n-1)$ points where $f'(x)=m$
Therefore, there exist at least $(n-2)$ points where $f''(x)=0$ (using Rolle's theorem).