Find the critical points of the function and determine whether the critical point is a local minimum or maximum (or neither). (Enter your answers as a comma-separated list. I answer does not exist, enter DNE.)
f(x) = 8x2 - 9x3 + 3
Find the points of inflection of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
Determine the intervals on which the function is concave up or concave down. (Enter your answers using interval notation. Enter EMPTY or 0 for the empty set.)
Water is pumped into a sphere on the figure below at a variable rate in such a way that the water level rises at a constant rate c = √3. When the water level in a sphere of radius R is h, the volume of water is V = π(Rh2 - h3/3).
What is the inflection point for V?