At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I solved for x and got x = 0, 9, -8 Not sure what to do from there.
so you solved x^3 - x^2 - 72x = 0 for x and you got x = 0, x = 9, x = -8 ??
ok first draw a number line and plot those three values on it |dw:1440998491371:dw|
label the different regions A,B,C,D |dw:1440998552769:dw|
x^3 - x^2 - 72x factors to x(x-9)(x+8) then set up a sign chart where the factors are written in a column on the left side the regions are written along the top row like this |dw:1440998659579:dw|
now let's pick a number from region A this could be any number you want as long as it's less than -8. So let's pick -9 if x = -9, then the sign of x is negative. We put a negative sign/symbol in the first row, first column like this |dw:1440998809112:dw|
keep x = -9 the same what is the value of x-9? that is x-9 = -9-9 = -18 which is also negative so place a negative symbol in the "A" column and "x-9" row |dw:1440998838462:dw|
if x = -9, then x+8 = -9+8 = -1 which is also negative |dw:1440998879510:dw|
I'm going to let y = x^3 - x^2 - 72x and write "y" in the bottom of the left most column |dw:1440998908837:dw|
to find the sign of y for column A (is y positive or negative?) we multiply the signs in column A negative*negative*negative = positive*negative = negative so ultimately, y is negative when x < -8, ie in region A |dw:1440998977212:dw|
So I did all the work and got x <- 8 -8 < x < 0 x > 9 Is this right?
does the sign chart make sense? if so, then go ahead and fill out the rest of it so I can see what you got
I figured out how to use the chart and made sense to me. So I got the answers that I wrote above.
you should have this sign chart |dw:1441000190738:dw|
take a few moments to check what I got to make sure you got the same things
did you get the same table?
ok great, just checking
notice how we want to solve for x in `x^3 - x^2 - 72x > 0` which is the same as `y > 0` since I made `y=x^3 - x^2 - 72x`
look in the chart when y > 0 ie when there's a + sign in the y row |dw:1441001180490:dw|
that corresponds to the intervals `-8 < x < 0` and `x > 9` |dw:1441001210042:dw|
so the solution to `x^3 - x^2 - 72x > 0` is `-8 < x < 0` OR `x > 9` we write \[\Large (-8, 0) \cup (9, \infty)\] if we wanted to state the entire solution set in interval notation the graph confirms all this https://www.desmos.com/calculator/6qe6nf0jao
Wow just wow *clap clap clap* Absolutely brilliant! Thanks for your time and help man, really appreciate it.
I'm glad it's all clicking now