Given the graph of h(x) (Attached Below), sketch the graphs of h'(x) and h''(x).
Please correct me if I am mistaken but I believe given the graph of h(x), the graph of the first derivative would be a parabola (opening up) with a minimum point at the coordinates (0,2) because there is a point of inflection on h(x) at x=2 and it is a continuously increasing function in the presented domain.
But is there anything other than that we can deduce about the graph of the first derivative given h(x)? Like the y-intercept for example? How accurate can my sketch be?
Thanks in advance.