2 Attachment(s)

The Second Derivative: A graphical look.

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 h(x), the graph of the first derivative would be a parabola (opening up) with a minimum point at the coordinates (0,2) because the point of inflection on h(x) is at x=2 and it is a continuously increasing interval in the domain presented.

But is there anything other than that we can deduce about the graph of the derivative given h(x)? Like the y-intercept for example? How accurate can my sketch be?

Thanks in advance.

Sincerely,

Raymond MacNeil