Limits, Continuity & Differentiability
Continuity And Differentiability
nta_abhyas_2025
Grade 12
Question:
The number of points at which the function $f(x) = |x - 0.5| + |x - 1| + \tan x$ is not differentiable in the interval $(0, 2)$ is/are
Step-by-Step Solution
Key Concept: Points of non-differentiability include sharp corners (cusps) and points of discontinuity
The curve has sharp corners at $x = 0.5$ and $x = 1$ and a point of discontinuity at $x = \frac{5}{2}$. Thus, the total number of points where the function is not differentiable is 3.
Correct Answer: 3