Question
Asked Dec 9, 2019
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Find all relative extrema of the function 2x^4 - 8x^3 + 6. Use the Second Derivative Test where applicable.

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Expert Answer

Step 1

Find y' and y" using exponent rule.

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y=2x*-8x³+6 y'=2(4x³)-8(3x²)+0 y'=8x³-24x² y"=8(3x²)-24(2x) y"=24x²-48x

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Step 2

For critical points y'=0 

From there find x.

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y'=0 8x -24x²=0 8x° (х-3)-0 8x²=0 х?—0 x=0 x-3=0 x=3

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Step 3

Plug x=0 and x=3 in y", to check which is maximum and which is ...

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y"=24x²-48x y"=24(0)²-48(0)=0 y"=24x?-48x y"=24(3)²-48(3) y"=24(9)-144 y"=216-144 y"=72

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