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Absolute Maximums and Minimums

Absolute Maximums and Minimums

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Tutorial

Defining and finding Absolute Maximums and Minimums

A few problems on absolute extrema

Find the Absolute Maximum and Absolute Minimum on each interval.

1.  f open parentheses x close parentheses equals 4 x squared minus 12 x plus 10 space o n space space space space open square brackets 1 comma 2 close square brackets

2.  f open parentheses x close parentheses equals fraction numerator 3 x over denominator square root of 4 x squared plus 1 end root end fraction space o n space open square brackets negative 1 comma 1 close square brackets space

3.  f open parentheses x close parentheses equals x minus 2 sin open parentheses x close parentheses space space o n space space space space open square brackets negative straight pi over 4 comma straight pi over 2 close square brackets

4.  f open parentheses x close parentheses equals open vertical bar 6 minus 4 x close vertical bar space space o n space space space space open square brackets negative 3 comma 3 close square brackets

Source: Calculus Early Transcendentals by Anton

Finding Absolute Maximums and Minimums on open intervals

Problems on Finding Absolute Extrema on Open Intervals

Find the Absolute Maximum and Absolute Minimum on each interval, if it exists.

5.  f open parentheses x close parentheses equals 3 minus 4 x minus 2 x squared space space o n space space space space open parentheses negative infinity comma plus infinity close parentheses

6.  f open parentheses x close parentheses equals fraction numerator x minus 2 over denominator x plus 1 end fraction space space o n space space left parenthesis negative 1 comma 5 right square bracket  

Source: Calculus Early Transcendentals by Anton