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Absolute maximum absolute minimum - PowerPoint PPT Presentation

Definitions:

Definitions:

Definitions:. If f : D -> K is a function and a is in D, then f(a) is a absolute minimum on D iff f(a) <= f(x), for every x in D. If f : D -> K is a function and a is in D, then f(a) is a absolute maximum on D iff f(x) <= f(a), for every x in D.

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4.1 Extreme Values of Functions

4.1 Extreme Values of Functions

4.1 Extreme Values of Functions. Borax Mine, Boron, CA Photo by Vickie Kelly, 2004. Greg Kelly, Hanford High School, Richland, Washington. 4.1 Extreme Values of Functions. Borax Plant, Boron, CA Photo by Vickie Kelly, 2004. Greg Kelly, Hanford High School, Richland, Washington.

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4.1 Extreme Values of Functions

4.1 Extreme Values of Functions

4.1 Extreme Values of Functions. Borax Mine, Boron, CA Photo by Vickie Kelly, 2004. Greg Kelly, Hanford High School, Richland, Washington. 4.1 Extreme Values of Functions. Borax Plant, Boron, CA Photo by Vickie Kelly, 2004. Greg Kelly, Hanford High School, Richland, Washington.

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4.1 Extreme Values of Functions

4.1 Extreme Values of Functions

4.1 Extreme Values of Functions. Greg Kelly, Hanford High School Richland, Washington. The mileage of a certain car can be approximated by:. At what speed should you drive the car to obtain the best gas mileage?. The textbook gives the following example at the start of chapter 4:.

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4.6 Minimum and Maximum Values of Functions

4.6 Minimum and Maximum Values of Functions

4.6 Minimum and Maximum Values of Functions. Borax Mine, Boron, CA Photo by Vickie Kelly, 2004. Greg Kelly, Hanford High School, Richland, Washington. Extreme values can be in the interior or the end points of a function. No Absolute Maximum. Absolute Minimum. Absolute Maximum.

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More about Extrema

More about Extrema

More about Extrema. Relative Extrema. Relative Maximums. Relative Minimums. Also called Local Extrema Also called Saddle Points. Absolute Extrema. Absolute Maximum. Absolute Minimum. Also called global maximum and global minimum. Critical Points of f.

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Part (a)

Part (a)

Area = (e x - ln x) dx. 1. 1/2. y = e x. 2. 1. -1. 1. y = ln x. Part (a). = 1.222 or 1.223. 4. 3. 2. 1. 1. 2. V = p [(4 - ln x) 2 - (4 - e x ) 2 ] dx. 1. 1/2. Part (b). To find the volume, we need to use the washer method. R = (4 - ln x) r = (4 - e x ).

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