Question

Let f:(0,1)→R be the function defined as f(x)=4x2(x-$\frac{1}{2}$), where [x] denotes the greatest integer less than or equal to x . Then which of the following statements is(are) true?

• A. The function f is discontinuous exactly at the point in (0,1)
• B. There is exactly one point in (0,1) at which the function f is continuous but not differentiable
• C. the function f is not differentiable at more than three points in (0,1)
• D. The minimum value of the function f is$-\frac{1}{512}$

Answer 1

Answer: (A), (B)

The function f is discontinuous exactly at the point in (0,1)

Answer 2