Extrema on an Interval
Learn about extrema on intervals, including absolute extrema and relative extrema, and how to find them using critical numbers. Explore the concept of maximum and minimum points on closed intervals and how to identify them analytically or with a calculator. Dive into homework exercises to practice and solidify your understanding of extrema in calculus.
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Presentation Transcript
3.1 Extrema on an Interval p. 212
Extrema the highest and lowest points on an interval. also called absolute extrema extrema are y-values
if f is continuous on a closed interval, then it must have an absolute maximum and and absolute minimum.
Relative Extrema highest/lowest point on an open interval can also be an absolute max/min
abs. max relative max abs. min relative min
Critical Number where the derivative equals zero or undefined (i.e. zeros of top and bottom). relative extrema occur only at critical #s.
How to find Absolute Max/Min on closed interval 1. find critical #s 2. evaluate f at critical #s and endpoints 3. highest value is abs. max, lowest value is abs. min
Finding extrema with a calculator Find the absolute extrema for .
Homework p. 217 11-19 odd, 23-43 EO odd, 51, 55, 74-77 all
