question 1: If the graph of the derivative of f (x) is shown, on which intervals would f (x) be concave up?
<a> (p, r)
<b> (r, s)
<c> (p, q)
<d> (q, s)
Concavity is told by the second derivative (the slope of the graph of the slopes of the tangent lines).Originally Posted by bobby77
I think the simplest way to analyze these are in terms of the way my Math teacher first presented it: The graph is "concave up" when you can pour water into it and the water doesn't pour back out. If the water would spill out, it's concave down. (There are examples where this won't work, such as the graph of y = x^3, but it works well as a "quick and dirty" method.)
Looking at the interval (r,s) it looks like that could hold some water (ignoring the open right side of the graph!). So (r,s) is concave up.