swin2013
Second derivative test to find the local extrema for the function?



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swin2013
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y = x^580x+100

timo86m
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i think it has to do with finding the f''(x)=0

swin2013
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I know that

swin2013
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y'(x) = 5x^4 80

abb0t
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\[y' = 5x^4 8\]
\[y'' = 20x^3\]

swin2013
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y''(x) = 20x^3

abb0t
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set y'' = 0 and solve.

swin2013
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i got 0... so i wasn't sure if that's right

swin2013
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0 = 20x^3

abb0t
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Yes.

swin2013
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Okay thanks!

swin2013
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Oh i forgot, is it the local minimum (x=0)?

swin2013
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@abb0t

abb0t
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If the second derivative is zero then the critical point can be anything. Look @ the graph of ur function.

swin2013
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so it's just the local extrema is located at x=0

swin2013
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and if it's like... 3 and 3 as the local extrema. I don't know if it's a local max or min correct?

abb0t
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Only if it's zero.
if < 0 = relative min
if > 0 = relative max.

swin2013
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ohhhh ok! Thank you so much!