Find the interval(s) where the function is increasing and the interval(s) where it is decreasing. (Enter your answers using interval notation.

Question

F(x)= (5/3)x³ - (15/2)x²

what are the intervals when increasing if any and decreasing if any

increasing=

decreasing=

Answer 1

So Ernesto M.,

Is it possible that you don't know what the derivative of a function is? If you do know, take the first derivative of the function, and set that expression equal to zero. Solve. There might be several solutions! Don't miss any. That will tell you the points where the slope reverses (ascending vs. descending). At those points, the slope is zero, so they are NOT included as the endpoints of the ascending or descending intervals. Put in a trial value between those points, to check whether ascending (positive y ') or descending (negative y'). Don't forget to take points outside your set of zero-slope-points, to make sure your intervals to +/- infinity are correctly ascribed.

If you DON'T know what the derivative of a function is, please consider some one-on-one tutoring help, from a peer, sib, older-student, parent, teacher, tutor, etc. You need to do a lot of catching up, but then you'll be OK.

When you get better at this, you'll be able to just scan the parent fnction and say: "highest power of x term rules the extreme ranges, so they are both ascending; there's a lower-power "minus" term in the expression, so there will be one descending region between somewhere." But you'll still have to differentiate to find out exact values for turn-arounds.

--Cheers, --Mr. d.