Question
Question: A continuous and differentiable function y = f(x) is such that its graph cuts line y = mx + c at n d...
A continuous and differentiable function y = f(x) is such that its graph cuts line y = mx + c at n distinct points,. Then the minimum number of points at which f ′′ (x) = 0 is/are
A
n – 1
B
n – 3
C
n – 2
D
Cannot say
Answer
n – 2
Explanation
Solution
From LMVT there exist atleast (n – 1) point where f ′(x) = m.
⇒ ∃ atleast (n – 2) points where f ′′(x) = 0
(using Rolle's theorem)