mad011
Determine all the critical points for the function f(x)= x^2 + (16/x)
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freckles
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You found f' yet?
mad011
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f '= 2x-(16/x^2)???
freckles
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Yep! :)
freckles
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Now combine fractions! :)
freckles
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\[f'=\frac{2x(x^2)-16}{x^2}\]
right? :)
mad011
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Thats what I got! :)
freckles
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Now set Mr.top=0! :) and solve for x
We would look at where the bottom is 0 except our function is not even define for x=0
So we are only look for when the top of f' is 0
freckles
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\[2x(x^2)-16=0\]
freckles
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Can you solve this for x?
mad011
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x=2 ??
freckles
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\[2x^3-16=0\]
Yes that is the only real critical number
\[x^3-8=0 \]
\[(x-2)(x^2+2x+4)=0\]
x=2
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\[b^2-4ac=2^2-4(1)(4)=4-16=-12 <0 => x=2 \text{ is the only critical number}\]
:)
So good job! :)
mad011
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Oh great! thank you
freckles
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You deserve a medal! Seriously great job! :)