Let a ∈ ℤ and t be the greatest integer ≤ t , then the number of points, where the function f x = a + 13   sin x ,   x ∈ 0 , π is not differentiable, is _ _ _ _ _ _ _ _ _ _ _ _

Step-by-step solution

Given, f x = a + 13   sin x ,   x ∈ 0 , π ⇒ f ( x ) = [ 13   sin x ] + a , as a ∈ Integer Now let g ( x ) = 13   sinx , now plotting the diagram of y = 13 sin x we get, Now from above diagram we can see that, f ( x ) = 13   sinx is not differentiable at intersection points of y = k ,   k ∈ [ 1 , 13 ]   &   k ∈ Z ⇒ Points of non-differentiability = 12 × 2 + 1 = 25