Download presentation

1
**Maxima and minima of functions**

Lesson 2.2

2
Definitions Global extrema: If f(c) ≥ f(x) for all x in the domain of f, f(c) is the global maximum value of f. If f(c)≤ f(x) for all x in the domain of f, f(c) is the global minimum value of f. Local extrema: If f(c) ≥ f(x) for all x in some open interval containing c, f(c) is a local maximum value of f. If f(c)≤ f(x) for all x in some open interval containing c, f(c) is a local minimum value of f.

3
Example 1: Y = button Approximate the global and local maximum and minimum on each given domain for the function k defined by k(x) = -2x4 + 3x3 + 4x2 – 5x + 5 Set of all real numbers: -1 ≤ x ≤ 1 x < -2

4
k(x) = -2x4 + 3x3 + 4x2 – 5x + 5 Set of all real numbers: -no global min, local min. at x≈ .477, k(x) ≈3.747 - local/global max. at x ≈-.865, k(x) ≈9.257, - local max. at x ≈ 1.513, k(x) ≈

5
k(x) = -2x4 + 3x3 + 4x2 – 5x + 5 -1 ≤ x ≤ 1 -local/global min at x≈ .477, k(x) ≈3.747 -local min at endpoint x=-1, k(x) = 9 -local/global max. at x ≈-.865, k(x) ≈9.257, - local max at endpoint, x = 1, k(x) = 5

6
k(x) = -2x4 + 3x3 + 4x2 – 5x + 5 x < -2 - there is no minimum since the function decreases without bound on the interval (-∞, -2). -There is no maximum because k(x) increases as x increases and there is no greatest value of x on this interval.

7
**Find the extrema of f(t)=2t4 +4t + 1**

Over [0,∞) - local/global min: t=0, f(t) = 1 - No local/global max. Over (-3,1): -local/global min: t≈-.787, f(t) ≈ -No local/global max.

8
Homework Page 91 3, 5, 6, 7 10, 12, 14

Similar presentations

Presentation is loading. Please wait....

OK

1 Concavity and the Second Derivative Test Section 3.4.

1 Concavity and the Second Derivative Test Section 3.4.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google