Consider the function f x = m a x 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 3 5 is

Step-by-step solution

Using graph of sin ⁡ x & cos ⁡ x , we get, f x is non differentiable at x 1 = π 4 ,   x 2 = 3 π 4 ,   x 3 = 5 π 4 , x 4 = 7 π 4 ,   x 5 = 9 π 4 ,   x 6 = 11 π 4 Hence, λ = 6