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

Question

Consider the function f(x)=max |sin x| , |cos ⁡ x| ∀ x∈ [0,3 π ] . If λ is the number of points at which f(x) is non-differentiable, then the value of λ is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Using graph of |sin x| &|cos â¡ x| , we get, f(x) is non differentiable at <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-g2uxxho5znslaxeb.jpg" /> x1=(π /4),x2=(3 π /4),x3=(5 π /4), x4=(7 π /4),x5=(9 π /4),x6=(11 π /4) Hence, λ =6

Q. Consider the function $f (x) = ma x {∣ s in x ∣, ∣ cos x ∣}, \forall x \in [0, 3 π]$ . If $λ$ is the number of points at which $f (x)$ is non-differentiable, then the value of $λ$ is

Using graph of $∣ s in x ∣ & ∣ cos x ∣$ , we get,
$f (x)$ is non differentiable at

$x_{1} = \frac{π}{4}, x_{2} = \frac{3 π}{4}, x_{3} = \frac{5 π}{4},$ $x_{4} = \frac{7 π}{4}, x_{5} = \frac{9 π}{4}, x_{6} = \frac{11 π}{4}$
Hence, $λ = 6$

Q. Consider the function f(x)=max{∣sinx∣,∣cos⁡x∣},∀x∈[0,3π] . If λ is the number of points at which f(x) is non-differentiable, then the value of λ is

Using graph of ∣sinx∣&∣cos⁡x∣ , we get, f(x) is non differentiable at x1​=4π​,x2​=43π​,x3​=45π​, x4​=47π​,x5​=49π​,x6​=411π​ Hence, λ=6

Q. Consider the function $f (x) = ma x {∣ s in x ∣, ∣ cos x ∣}, \forall x \in [0, 3 π]$ . If $λ$ is the number of points at which $f (x)$ is non-differentiable, then the value of $λ$ is

Using graph of $∣ s in x ∣ & ∣ cos x ∣$ , we get,
$f (x)$ is non differentiable at

$x_{1} = \frac{π}{4}, x_{2} = \frac{3 π}{4}, x_{3} = \frac{5 π}{4},$ $x_{4} = \frac{7 π}{4}, x_{5} = \frac{9 π}{4}, x_{6} = \frac{11 π}{4}$
Hence, $λ = 6$