section 4.1 maxima and minima 1. 2 3 4 a.satisfies the conditions of the extreme value theorem....
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Section 4.1
Maxima and Minima
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a. Satisfies the conditions of the Extreme Value Theorem. Absolute maximum at x = a and absolute minimum at x = c.
Absolute maximum at x = c
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Absolute maximum: q and sLocal maximum: q and s
Absolute minimum: pLocal minimum: p and r
If f has a local maximum or minimum at cand f’(c) exists, then f’(c) = 0.
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Note the converse of Theorem is not necessarily true.
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X(2ln x + 1) = 0; x = 0 not in domain
or 2ln x + 1 = 0 ln x = -1/2 x = e-1/2 ≈ 0.61
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f(-2) = 32 absolute maximum
f(3/2) = -27/16 absolute minimum
a. 22 0 2 3 0
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x x
x x critical values
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b.
g(-1) = 3 absolute maximum and g(0) = g(2) = 0 absolute minimum
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SOLUTION
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