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Let g be a differentiable function such that for all and . Determine if and are relative extrema. Justify your answer. Homework Help ✎

Determine if is an extrema candidate.
That is, does or does DNE

(some negative value)
Yes, f(3) is an extrema candidate! It could be a relative max, a relative min, or neither.

Determine if f(3) is a relative max, relative min or neither. Use the 1st-derivative test:
To do this, determine if changes sign at .
Evaluate a little to the left and a little to the right.
To the left: (some negative value) (negative)(negative) positive.
To the right: (some negative value) (positive)(negative) negative.
Conclusion: Since and changes from positive to negative at , therefore is a relative maxima.

Now test .