Thread: 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.

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





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

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

is where it is decreasing

You said it yourself: x is between 0 and 2. This statement about an interval is commonly written as or 0 < x < 2.

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

To find concavity use the second derivative test

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?

Try I think that is the answer because it wants when concave up and decreasing.