Let f x = 4 x 2 - 8 x + 5 , if   8 x 2 - 6 x + 1 ≥ 0 4 x 2 - 8 x + 5 , if   8 x 2 - 6 x + 1 < 0 , where α denotes the greatest integer less than or equal to α . Then the number of points in R where f is not differentiable is _____ .

Step-by-step solution

Given, f x = 4 x 2 - 8 x + 5 , if   8 x 2 - 6 x + 1 ≥ 0 4 x 2 - 8 x + 5 , if   8 x 2 - 6 x + 1 < 0 = 4 x 2 - 8 x + 5 , if   x ∈ − ∞ , 1 4 ∪ 1 2 , ∞ 4 x 2 - 8 x + 5 if   x ∈ 1 4 , 1 2 ⇒ f x = 4 x 2 − 8 x + 5 if   x ∈ − ∞ , 1 4 ∪ 1 2 , ∞ 3 x ∈ 1 4 , 2 − 2 2 2 x ∈ 2 − 2 2 , 1 2 Now plotting the graph of f x we get, We can see f x is not differentiable at 1 4 , x 1 , 1 2 (where x 1 =