If `f(x)` is a differentiable function at a point `a` and `f' (a) != 0`, then which of the following statements is true

If the function F: R to R is defined by f(x)=|x|(x-sinx) , then which o f the following statemnts is true ?

Let f(x) be twice differentiable function for all real x and f(1) = 1, f(2) = 4 , f(3) = 9. Then which one of the following statements is definitelly true ?

For function f(x)=(lnx)/(x), which of the following statements are true?

For function f(x)=(lnx)/(x), which of the following statements are true?

If f(0)=f(1)=f(2)=0 and function f(x) is twice differentiable in (0, 2) and continuous in [0, 2], then which of the following is/are definitely true ?

If f(0)=f(1)=f(2)=0 and function f(x) is twice differentiable in (0, 2) and continuous in [0, 2], then which of the following is/are definitely true ?

If f(0)=f(1)=f(2)=0 and function f(x) is twice differentiable in (0, 2) and continuous in [0, 2], then which of the following is/are definitely true ?

If f(0)=f(1)=f(2)=0 and function f(x) is twice differentiable in (0, 2) and continuous in [0, 2], then which of the following is/are definitely true ?

If f(x) is a differentiable function satisfying |f'(x)|le4AA x in [0, 4] and f(0)=0 , then