# Thread: decreasing function and concavity

1. ## decreasing function and concavity

On what intervals is the function f(x)=x3−3x 2

decreasing and concave up

i took the derivative and got 3x^2-6x. Then i found the zeroes which are x=0,2. I checked where the function was decreasing and i got (-infinity,1] but it keeps saying its wrong. I don't get why.

2. The function is decreasing when the derivative is less than zero. Using your correct calculation of the derivative:

$3x^2 - 6x < 0$

$3x(x - 2) < 0$

Now you can analyze the derivative to find out where it is negative. On what interval(s) is it negative?

3. so the function is increasing when x<0, decreasing between 0 to 2, and increasing when x>2. I still don't get how to write the interval

4. $(0,2)$ is where it is decreasing

5. You said it yourself: x is between 0 and 2. This statement about an interval is commonly written as $x \in (0, 2)$ or 0 < x < 2.

6. it said (0,2) was wrong. i tried that already.

7. To find concavity use the second derivative test

8. Originally Posted by jojoferni244
it said (0,2) was wrong. i tried that already.
Did you try entering in the answer the way icemanfan said?

9. Try $(1,2)$ I think that is the answer because it wants when concave up and decreasing.