2.10 Functions & Derivatives

For the graph above, at point A:

• f' is positive, f" is positive

• f' is positive, f" is negative

• f' is negative, f" is positive

• f' is negative, f" is negative

For the graph above, at point B:

• f' is positive, f" is positive

• f' is positive, f" is negative

• f' is negative, f" is positive

• f' is negative, f" is negative

For the graph above, at point C:

• f' is positive, f" is positive

• f' is positive, f" is negative

• f' is negative, f" is positive

• f' is negative, f" is negative

If f has a point of inflection, then f' is:

• increasing

• positive

• = 0

• a max or a min

If f has an inflection point, then f"

• has a max or min

• = 0

• no information is known

If f is concave down, then f' is:

• decreasing

• negative

if f is decreasing, then f"

• is negative

• has a max or min

• is concave down

• no information is known

If f is increasing, then f' is

• increasing

• decreasing

• positive

• negative

If f" = 0, then f'

• has an inflection point

• has a max or min

• has an x-intercept

If f" is negative, then f' is

• increasing

• decreasing

• concave up

• concave down