05Minimum and Maximum Problems - MINIMUM AND MAXIMUM...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
M INIMUM AND M AXIMUM P ROBLEMS Abs. min but no no absolute extrema both an abs. max and abs max on ) , ( -∞ on ) , ( -∞ abs min on ) , ( -∞ a b a b Both abs. max and none on [ ] b a , both on [ ] b a , min on [ ] b a , a b ) ( x f is not continuous on [ ] b a , so no abs. To find the absolute extrema of a continuous function f on a finite closed interval [ ] b a , . 1. Find the critical numbers of f in ( 29 b a , . 2. Evaluate f at all the critical numbers and at the endpoints a and b. 3. The largest of these values is the absolute max, the smallest is the absolute min. Applied Problems: Step 1: Draw and label a picture. Step 2: Find a formula for the quantity to be maximized or minimized. Step 3: Express the quantity as a function of 1 variable. Step 4: Find the restrictions. Step 5: Find the max or min. Extreme-Value Theorem : If a function f is continuous on a finite closed interval [ ] b a , , then f has both an absolute maximum and an absolute minimum on [ ] b a , .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

05Minimum and Maximum Problems - MINIMUM AND MAXIMUM...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online