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Relative Min & Max

Relative Min & Max

I'm asked to determine the relative min and/or relative max for the function:

f(x)=x^3-x^2-x+2

How do I do this? Am I being asked to find the derivative of this function?
1 REPLY 1

Relative Min & Max


>I'm asked to determine the relative min and/or relative max for the function:
>
>f(x)=x^3-x^2-x+2

Find the first derivative:

f'(x) = 3�x^2 - 2�x - 1
Find values for x such that f'(x) is zero.
Factoring gives x = -1/3 and x = 1
These are the POSSIBLE relative extrema.

Find the second derivative:

f"(x) = 6�x - 2

Determine the curvature at the POSSIBLE relative extrema.

f"(-1/3) = -4 -- Negative, making a relative maximum

f"(1) = 4 -- Positive, making a relative minimum.

If you wish to knew the value fo the relative extrema, you must evaluate the original function at those points, f(-1/3) and f(1).
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