Consider the function
$$f(x) = 12x^5 + 45x^4 - 200x^3 + 4.$$
f(x) has inflection points at (reading from left to right) x = D, E, and F
where D is
and E is 0
and F is
For each of the following intervals, tell whether f(x) is concave up or concave down.
$$(-\infty, D):$$ Concave Down
$$(D, E):$$ Concave Up
$$(E, F):$$ Concave Down
$$(F, \infty):$$ Concave Up