JEE Mains · Maths · STD 12 - 5. continuity and differentiation
The number of points, at which the function \(f(x) = \max\{6x, 2 + 3x^2\} + |x - 1|\left|\cos\left|x^2 - \dfrac{1}{4}\right|\right|\), \(x \in (-\pi, \pi)\), is not differentiable, is _____.
- A 9
- B 18
- C 27
- D 36
Answer & Solution
Correct Answer
(A) 9
Step-by-step Solution
Detailed explanation
Let \(f(x) = g(x) + h(x)\), where \(g(x) = \max\{6x,\ 2 + 3x^2\}\) \(h(x) = |x - 1|\left|\cos\left|x^2 - \dfrac{1}{4}\right|\right|\) We find the points of non-differentiability of each part in \(x \in (-\pi, \pi)\). Non-differentiability of \(g(x)\):…
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