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- anonymous

How can you find the intervals on which f is increasing and decreasing when f(x)=(x^4)-(4x^3)+(4x^2)

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- anonymous

How can you find the intervals on which f is increasing and decreasing when f(x)=(x^4)-(4x^3)+(4x^2)

- schrodinger

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- IsTim

Solve for x I guess. You know how to do that, right? Then, you make a chart with the data...

- anonymous

all i did so far was find the derivative and replaced f(x) with 0

- anonymous

and found x= 0, 5, and -1

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- IsTim

Ok. Those will be your interval points. They go: (infinity,o)(0,5) and (5,-1)

- IsTim

To find the y-int, sub in x=0

- anonymous

what do you mean?

- IsTim

|dw:1327657008314:dw| I mean that you make x=0 to for the y-intercept.

- anonymous

After you find the derivative equate it to 0 and solve for x, then substitute the 3 values you get into the given function. Now if it is negative,it has a max at that point and is therefore going to decrease in that interval whilst if it is positive it is a min and therefore it is going to increase in that interval.

- anonymous

http://www.wolframalpha.com/input/?i=f%28x%29%3D%28x%5E4%29-%284x%5E3%29%2B%284x%5E2%29

- campbell_st

I'd graph the curve find the zeros, x=0, 2 are the zeros.... found by factorising
next find the 1st derivative..... and find the stationary points...
next find the 2nd derivative and any possible points of inflexion....
test the 1st derivative points in the 2nd derivative to test concavity... draw the graphs... and read the intervals off...

- anonymous

i got it, thanks everyone

- IsTim

Good work everyone. BATMAN AWAY

- anonymous

lol

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