How would i solve this?
f(x) = x^3+ax^2 + bx +c

a. over what interval f concave up? concave down?
b. show that f must have exactly one flection point.
c. given the (0,-2) is the inflection point of f, compute a and c and then show that f has no critical point

Question

How would i solve this?
f(x) = x^3+ax^2 + bx +c

a. over what interval f concave up? concave down?
b. show that f must have exactly one flection point.
c. given the (0,-2) is the inflection point of f, compute a and c and then show that f has no critical point

anonymous · Answer

it is concave up when the second derivative is positive and concave down when the second derivative is negative
inflection points are where the second derivative crosses the x-axis so since the second derivative is always increasing it only does this once
use the fact that the second derivative is 0 at inflection points to solve for a and then plug in x = 0 and y = -2 into the original equation to solve for c