4.1- Maxima and Minima

Question 1

Two things guarantee an absolute extreme exists

Answer 1

The function must be continuous on the interval and the interval must be closed and bounded

Question 2

Extreme Value Theorum

Answer 2

A function that is continuous on a closed interval [a,b] has an absolute maximum and an absolute minimum value on that interval

Question 3

Local Extreme Point Theorum

Answer 3

If f has a local maximum or minimum value at c and f’(c) exists, then f’(c) = 0

Question 4

Is it possible for f’(c) to be zero without a local maximum or minimum

Answer 4

yes. Think of x to the third graph

Question 5

Find the critical points of f(x)= x/(x^2 +1)

Answer 5

Set f’(x) to zero and wherever the derivative is zero. Those are your critical points

Question 6

The procedure for locating maximum and minimum values

Answer 6

1. Locate the critical points c in (a,b), where f’(c)= 0 OR f’(c) does not exist.
2. Evaluate f at the critical points and at the end points of the interval
3. Choose the largest and smallest values from Step 2 for the absolute maximum and minimum values

Question 7

Find the Absolute extreme values on the interval

x^4 - 2x^3 on the interval [-2,2]

Answer 7

do it