Let f x -sin x -cos x -sin x - cos x - x -0-2 - then the number of points of non-differentiability of f x is

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Standard XII

Mathematics

Extrema

Let f x =sin ...

Question

Let $f (x) = sin x + | cos x | - ∣ ∣ s i n x - | c o s x | ∣ ∣$ , $x ϵ (0, 2 π)$ then the number of points of non-differentiability of $f (x)$ is

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Solution

As $a + b - | a - b | = 2 min {a, b}$
$∴ f (x) = min {2 sin x, 2 | cos x |}$

Hence, the given function is non derivable at $3$ points.

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Let f(x)=sinx+|cosx|−∣∣sinx−|cosx|∣∣, x ϵ(0,2π) then the number of points of non-differentiability of f(x) is

As a+b−|a−b|=2 min{a, b} ∴f(x)=min{2sinx,2|cosx|} Hence, the given function is non derivable at 3 points.

Let $f (x) = sin x + | cos x | - ∣ ∣ s i n x - | c o s x | ∣ ∣$ , $x ϵ (0, 2 π)$ then the number of points of non-differentiability of $f (x)$ is

As $a + b - | a - b | = 2 min {a, b}$
$∴ f (x) = min {2 sin x, 2 | cos x |}$

Hence, the given function is non derivable at $3$ points.