1. ## critical values

Hi guys, I was given a graph of the derivative or f ' (x), not f (x), which is where I am slightly confused on this problem... Given the graph of f '(x) answer questions about f(x)

a) for what values of x is the original function increasing/decreasing?
b) what values does original function, f(x) have horiz tangent lines?
c) what approx values of x does original function, f(x) have inflection points?

Here's what I have so far, but im not sure if I am doing this correctly for the values of the original function or for the graph of the derivative:
increasing at -infinity to -1.5 AND 1 To infinity
decreasing at -1.5 to 1
Horiz tangent lines at x=1 and -1.5
Inflection Points = none

2. So the graph shown is for the 1st derivative of f(x).

The function f(x) increasing if the 1st derivative is positive.
So, that is in the intervals (-2,-1) and (2, +infinity)
Or, from just after x = -2 to just before x = -1, and then, from just after x = 2 to positive infinity.

The function f(x) is decreasing if the 1st derivative is negative.
So that is from negative infinity to just before x = -2, then from just after x = -1 to just before x = 2.

f(x) has horizontal tangent lines where the 1st derivative is zero.
So those are at x = -2, x = -1 and x = 2.

f(x) has an inflection point where its 1st derivative is at maximum or minimum.
So those are at x = -1.5 and x = 1, if my eyes can see clearly.

3. thx ticbol, perfect explanation!