Chap4_Sec1

Chap4_Sec1 - MAXIMUM MINIMUM VALUES Example 4(4.1 You can see that f(1 = 5 is a local maximum whereas the absolute maximum is f-1 = 37 This

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
You can see that f (1) = 5 is a local maximum, whereas the absolute maximum is f (-1) = 37. s This absolute maximum is not a local maximum because it occurs at an endpoint. Also, f (0) = 0 is a local minimum and f (3) = -27 is both a local and an absolute minimum. s Note that f has neither a local nor an absolute maximum at x = 4. Example 4 (4.1)
Background image of page 1

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

View Full DocumentRight Arrow Icon
If f ( x ) = x 3 , then f ’ ( x ) = 3 x 2 , so f ’ (0) = 0. s However, f has no maximum or minimum at 0—as you can see from the graph. s Alternatively, observe that x 3 > 0 for x > 0 but x 3 < 0 for x < 0. The fact that f ’ (0) = 0 simply means that the curve y = x 3 has a horizontal tangent at (0, 0). s Instead of having a maximum or minimum at (0, 0), the curve crosses its horizontal tangent there. Example 5 (4.1) FERMAT’S THEOREM
Background image of page 2
f ( x ) = | x | has its (local and absolute) minimum value at 0. s However, that value can’t be found by setting f ’ ( x ) = 0. s
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/23/2011 for the course MAC 2311 taught by Professor Noohi during the Fall '08 term at FSU.

Page1 / 8

Chap4_Sec1 - MAXIMUM MINIMUM VALUES Example 4(4.1 You can see that f(1 = 5 is a local maximum whereas the absolute maximum is f-1 = 37 This

This preview shows document pages 1 - 4. Sign up to view the full document.

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