Question

f(x) = 2x3 + 3x2 − 432x
Part (a)
Find the intervals on which f is increasing. Find the interval on which f is decreasing.

Part (b)
Find the local minimum and maximum values of f.

Part (c)
Find the inflection point. Find the interval on which f is concave up. Find the interval on which f is concave down.

Answer 1

a) find f':
6x^2 + 6x - 432 = 0
then find where its positive, that is when f is increasing.

Answer 2

when its negative f will be decreasing, at 0 u will have local max and mins

Answer 3

c) f" = 12x + 6 = 0
12x+6 = 0 and the signs of f" change before and after that 0, then u have an inflection point

Answer 4

concave up - f" >0
concave down - f"<0, sorry i gtg just do all the steps above..

Answer 5

Thanks a lot really appreciate it.