If t denotes the greatest integer ≤ t , then number of points, at which the function f x = 4 2 x + 3 + 9 x + 1 2 - 12 x + 20 is not differentiable in the open interval - 20 , 20 , is ______.

Step-by-step solution

Given, f x = 4 2 x + 3 + 9 x + 1 2 - 12 x + 20 x ∈ - 20 , 20 Now we know that x is non-differentiable when x ∈ I So, 12 x + 20 is not differentiable at x = I ∈ - 19 , - 18 , … 0 , … 19 = 39 Now 9 x + 1 2 is not differentiable when x = I + 1 2 So, here also total non-differentiable points are 39 Now checking modulus function We know that modulus function are non-differentiable at point where modulus function is zero, So at x = - 3 2 modulus function is zero Also f x at x = - 3 2 is not