The number of points, at which the function , is not differentiable, is ________. [2026]

Question

The number of points, at which the function $f (x) = \max {6 x, 2 + 3 x^{2}} + | x - 1 | \cos | x^{2} - \frac{1}{4}], x \in (- π, π)$ , is not differentiable, is ________. [2026]

Smart Achievers · Accepted Answer

(3)

$f (x) = \max {6 x, 2 + 3 x^{2}} + | x - 1 | \cos | x^{2} - \frac{1}{4}]$

Sharp corner at $3 x^{2} + 2 = 6 x$

$\Rightarrow 3 x^{2} - 6 x + 2 = 0 \Rightarrow x = \frac{6 \pm \sqrt{36 - 24}}{6}$

$\Rightarrow x = \frac{3 \pm \sqrt{3}}{3} \Rightarrow x = 1 \pm \frac{1}{\sqrt{3}} \in (- π, π)$

$∴$ 2 points of non-differentiability

For $| x - 1 | \cos | x^{2} - \frac{1}{4} | : x = 1$ is the point of non-differentiability.

$∴$ Hence, total 3 points of non-differentiability.

Solution

Q.
The number of points, at which the function $f (x) = \max {6 x, 2 + 3 x^{2}} + | x - 1 | \cos | x^{2} - \frac{1}{4}], x \in (- π, π)$ , is not differentiable, is ________. [2026]

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Solution

Q. The number of points, at which the function f(x)=max{6x,2+3x2}+|x–1|cos|x2–14],x∈(–π,π), is not differentiable, is ________. [2026]

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Q.
The number of points, at which the function $f (x) = \max {6 x, 2 + 3 x^{2}} + | x - 1 | \cos | x^{2} - \frac{1}{4}], x \in (- π, π)$ , is not differentiable, is ________. [2026]