Consider the function f(x) = max\ | x|, | x|\ , x ∈ [0,3π] . If λ is the number of points at which f(x) is non-differentiable, then the value of λ ^ 3 5 is

Correct answer: 43.20 Using graph of | x| and | x|, we get, f(x) is non differentiable at x _ 1 = (π)/(4), x _ 2 = (3π)/(4), x _ 3 = (5π)/(4), x _ 4 = (7π)/(4), x _ 5 = (9π)/(4), x _ 6 = (11π)/(4) Hence, λ = 6

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Continuity and Differentiability

NTA Abhyas 2020 · Mathematics · Continuity and Differentiability

Consider the function f(x) = max\ | x|, | x|\ , x ∈ [0,3π] . If λ...

Consider the function

f\left(x\right) = max\left\{\left|\sin x\right|, \left|\cos x\right|\right\}, \forall x \in \left[0,3\pi\right]

. If

\lambda

is the number of points at which

f\left(x\right)

is non-differentiable, then the value of

\dfrac{{\lambda}^{3}}{5}

is $Consider the function f(x) = max\ | x|, | x|\ , x ∈ [0,3π] . If λ is the number of points at which f(x) is$

Correct answer

43.20

Step-by-step solution

Using graph of

\left|\sin x\right| \text{\text{ and } }

\left|\cos x\right|, we get,

f\left(x\right)

is non differentiable at
$Consider the function f(x) = max\ | x|, | x|\ , x ∈ [0,3π] . If λ is the number of points at which f(x) is$

{x}_{1} = \dfrac{\pi}{4}, {x}_{2} = \dfrac{3\pi}{4}, {x}_{3} = \dfrac{5\pi}{4}, {x}_{4} = \dfrac{7\pi}{4}, {x}_{5} = \dfrac{9\pi}{4}, {x}_{6} = \dfrac{11\pi}{4}

Hence,

\lambda = 6

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