Assume that a snowball melts so that its volume decreases at a rate proportional to its surface area. If it takes three hours for the snowball to decrease to half its original volume, how much longer will it take for the snowball to melt completely?

Calculus notes for the week of 10/3/16 4.1 Maxima and Minima and 4.2 What Derivatives Tell Us 15 10 5 01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 -5 -10 -15 f has a local maximum at c if f(c) > f(x) for all x sufficiently close to c. f has a local minimum at c if f(c) < f(x) for all x sufficiently close to c. We see that, if f is differentiable at a local extremum (c), then f’(c) = 0. It is impossible that f is not differentiable at a local extremum. Definition: f has a critical point at x if f ’(x) = 0 or f ’(x) DNE. Coordinates for local extremum will be critical points. We see that, if f ‘(x) is negative on an interval I, then f is decreasing on I. If f ‘(x) is positive on an interval I, then f is