Chapter 6, Problem 46RE

Suppose that f:R → R is a function with second derivative f"(x)=x•(x+ 1)³ • (x + 5)ª . Find intervals of concavity-up and concavity-down of f(x), and the x-coordinate(s) of any point(s) of inflection. Explain your answers.

Give an example of a differentiable function ƒ whose first derivative is zero at some point c even though ƒ has neither a local maximum nor a local minimum at c.

Let h be a twice-differentiable, decreasing function of t. If h(-5) = 40 and h(15) = –20, which of the following must be true on the interval (-5, 15) ? (A) h(t) is strictly decreasing on the interval. (B) h(t) has a tangent line with a slope of –3 for some t in the interval. (C) h(t) is concave down for all t in the interval. (D) h(t) is concave up for all t in the interval. A В