rnotchick
Find any critical numbers of the function f(x)=x^2(x^2−64).



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myininaya
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Find f'
Set f'=0

myininaya
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Solve f'=0 for x :)

rnotchick
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Dont you have to set the derivative equal to 0?

myininaya
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Yep.

rnotchick
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I am confused on what the derivative is of this

myininaya
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You know product rule you have a function times another function.
You have x^2 times (x^264)

myininaya
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\[(fg)'=f'g+fg' \]

rnotchick
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okay thats what i thought

rnotchick
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Then the two numbers that make that 0 are 0 and 8 i thought

myininaya
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You need to find [x^2(x^264)]'

myininaya
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You need to use the product rule....
Or!
You could distribute x^2 first then just use power rule for both terms.

rnotchick
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Okay after I have the derivative of that, what is the next step

rnotchick
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2x(x^264)+x^2(2x)

rnotchick
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?

myininaya
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Right! :)
Now set that equal to 0 and solve for x.