# Thread: Increasing and Decreasing Functions

1. ## Increasing and Decreasing Functions

I'm given the question:

"Suppose that "f" is a differentiable function with derivative f'(x) = (x-1)(x+2)(x+3). Determine where the function values of "f" are increasing and where they are decreasing."

A friend and I are trying to work out how to do this problem, and we're not having much luck. Our thoughts were to find the second derivative and then plugging in the x points from the first derivative to find where "f" is increasing or decreasing, but we're not having much luck.

Could some provide some insight as to the answer of this problem?

2. Originally Posted by Jeavus
I'm given the question:

"Suppose that "f" is a differentiable function with derivative f'(x) = (x-1)(x+2)(x+3). Determine where the function values of "f" are increasing and where they are decreasing."

A friend and I are trying to work out how to do this problem, and we're not having much luck. Our thoughts were to find the second derivative and then plugging in the x points from the first derivative to find where "f" is increasing or decreasing, but we're not having much luck.

Could some provide some insight as to the answer of this problem?
They have already done most of the hard work for you.

your critical numbers (where the function can change from increasing to decreasing) are the zero's of the derviatvie x= -2,-3,1

So just test points in each interval so see if f is increasing or decreasing

3. ## Just to let you know

if you imput any value into $f''(x)$ this will tell you nothing about the slope of $f(x)$...it will tell you about the slope of $f'(x)$...in other words the slope of the slope...which is known as concavity...and where concavity changes sign you have an inflection point