Let f(t) be a real-valued function whose second derivative is positive for -∞<t<∞. Which of the following statements is/are always true?

Consider the function f(t)=(max(0,t))2 for -∞<t<∞, where max(a,b) denotes the maximum of a and b. Which of the following statements is/are true?

Let f(x) be a real-valued function such that f'(x0)=0 for some x0∈(0,1) and f''(x)>0 for all x∈(0,1). Then f(x) has