Calculus Book: pp 190-199

Question 1

concavity

Answer 1

• The terms concavity and inflection point refer to the directionality of a curve. If a curve is concave up (convex), the graph of the curve is bent upward, like an upright bowl. … If , then x is an inflection point, where the graph changes direction of concavity.

Question 2

point of inflection

Answer 2

• In differential calculus, an inflection point, point of inflection, flex, or inflection (British English: inflexion) is a point on a curve at which the curve changes from being concave (concave downward) to convex (concave upward), or vice versa.

Question 3

second derivative test

Answer 3

• The second derivative may be used to determine local extrema of a function under certain conditions. If a function has a critical point for which f′(x) = 0 and the second derivative is positive at this point, then f has a local minimum here.

Question 4

limits at infinity

Answer 4

• However, the limit of f(x) as x approaches zero from the positive direction is positive infinity. The one-sided limit is defined because you are looking at what one side of the function is doing as the value of x moves toward zero from the right (or the positive direction).