Question

Let f(x)=3x^3−36x+3.
-On which interval is f increasing? Decreasing?
-Find the points at which f achieves a local min. and local max.
-Find intervals on which f is concave up and concave down.
-Find all points of inflection.

Answer 1

f(x)=3x^3−36x+3

-Find the points at which f achieves a local min. and local max.

so solve for f'(x) = 0

Answer 2

\[f'(x) = 9x^2 -36\]
Setting that equal to 0 I get x=2 and x=-2

Answer 3

How do I know which is a max. and which is a min. ? Do I plug it into the original function?

Answer 4

to find out if f is increasing or decreasing you plug in x=2 and x =-2 into the first derivative of the equation

Answer 5

increasing and decreasing comes from the first derivative
concave up and concave down comes from the second derivative.

Answer 6

for increasing and decreasing if your result after plugging in x = 2 or -2 is negative, we are decreasing. If your result after plugging in x =2 or -2 is positive, we are increasing.

Answer 7

local min and local max... well we need to grab the absolute max (highest point in the graph) and the absolute min (lowest point the graph) before dealing with that. local min is decreasing over a certain area in the graph and local max is increasing over a certain area in the graph

Answer 8

inflection point (omg hope I still remember this) is the point where the graph is switching from negative to positive or positive to negative.

Answer 9

this is just an example...