Question

A continuous and differentiable function $y=f\left(x\right)$ is such that its graph cuts line $y=mx+c$ at $n$ distinct points. Then the minimum number of points at which $f^{\prime \prime }\left(x\right)=0$ is/are

• A. $n-1$
• B. $n-3$
• C. $n-2$
• D. cannot say

Answer 1

The correct option is C $n-2$

$y=f\left(x\right)$ is a differentiable and continuous curve. The line cuts this curve n times so leave end cuts of curve and rest intersecting must be infection point. thus at least $n-2$ points are inflection points.