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lgove

Joined: Feb 21, 2009
Posts: 1
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Relative minimum of function

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Need help finding the relative minimum of the function:

f(x)= 2x^3-3x^2-12x-1

[Feb 24, 2009 1:12:14 PM]

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pskinner

Joined: Apr 2, 2005
Posts: 694
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Re: Relative minimum of function

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Need help finding the relative minimum of the function:

f(x)= 2x^3-3x^2-12x-1

If you enter 2x^3-3x^2-12x-1 into one of the function graphing calculators, you get not only the graph but also a complete tutorial on how to get the relative minimum.

First compute the derivative: f'(x)=6x^2-6x-12, set it equal to zero and solve for x:

6(x^2-x-2)=6(x-2)(x+1)=0

So, the relative extreme values occur at x=-1 and 2. As you read the graph from left to right, the cubic is rising, then falling, then rising, so x=2 is where the relative minimum occurs.
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Principal Skinner

[Feb 24, 2009 7:50:44 PM]

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