Question

Suppose that f(x)=x^3−3x^2+2.
where is the function increasing and where is it decreasing on what intervals. what is the point of inflection

Answer 1

hi first get the derivative

Answer 2

yeah i have the derivative i got 3x^2-6x

Answer 3

well find the critical points making the derivative equal to zero

Answer 4

so i set it equal to zero.. can you refresh my memory on how to use the first derivative test

Answer 5

looking at the first derivative like this 3x(x-2) will be easier to find the zeroes. find second derivative and set that equal to zero (same method as first) in order to find inflection points.

Answer 6

so for my critical point i got 0 and 2 is that correct

Answer 7

i had a question where to i plug in my critical points to find out where it increases and decreases

Answer 8

plug in your critical points into the second derivative.

Answer 9

when second derivative is positive it's a min., negative it's max

Answer 10

in order to find out inc and dec i thought that was for points of inflection

Answer 11

sorry to find out if its increasing or decreasing use the number line
e.g.