`f(x) ` is continuous at `x = 0` then which of the following are always true ?

Let f : [-3, 4] to R such that f ''(x) gt 0 for all x in [-3,4], then which of the following are always true ?

Let f : [-3, 4] to R such that f ''(x) gt 0 for all x in [-3,4], then which of the following are always true ?

If x = a, then which of the following is not always true for an integer k.

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(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) true ?

Function f(x), g(x) are defined on [-1, 3] and f''(x) > 0, g''(x) > 0 for all x in [-1, 3] , then which of the followingis always true ?