Calculus
Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 4, Problem 1PE
To determine

To write:The difference between absolute and relative extrema of a function.

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Explanation of Solution

Given information: The absolute and relative extrema of a function.

Relative extrema is the extreme point in function’s neighborhood and absolute extrema is the extreme points in its domain. A function can have a number of relative extremum but not more than one absolute extrema.

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A graph of the function f is given below: Study the graph of ƒ at the value given below. Select each of the following that applies for the value a = 1 Of is defined at a. If is not defined at x = a. Of is continuous at x = a. If is discontinuous at x = a. Of is smooth at x = a. Of is not smooth at = a. If has a horizontal tangent line at = a. f has a vertical tangent line at x = a. Of has a oblique/slanted tangent line at x = a. If has no tangent line at x = a. f(a + h) - f(a) lim is finite. h→0 h f(a + h) - f(a) lim h->0+ and lim h h->0- f(a + h) - f(a) h are infinite. lim does not exist. h→0 f(a+h) - f(a) h f'(a) is defined. f'(a) is undefined. If is differentiable at x = a. If is not differentiable at x = a.
The graph below is the function f(z) 4 3 -2 -1 -1 1 2 3 -3 Consider the function f whose graph is given above. (A) Find the following. If a function value is undefined, enter "undefined". If a limit does not exist, enter "DNE". If a limit can be represented by -∞o or ∞o, then do so. lim f(z) +3 lim f(z) 1-1 lim f(z) f(1) = 2 = -4 = undefined lim f(z) 1 2-1 lim f(z): 2-1+ lim f(x) 2+1 -00 = -2 = DNE f(-1) = -2 lim f(z) = -2 1-4 lim f(z) 2-4° 00 f'(0) f'(2) = = (B) List the value(s) of x for which f(x) is discontinuous. Then list the value(s) of x for which f(x) is left- continuous or right-continuous. Enter your answer as a comma-separated list, if needed (eg. -2, 3, 5). If there are none, enter "none". Discontinuous at z = Left-continuous at x = Invalid use of a comma.syntax incomplete. Right-continuous at z = Invalid use of a comma.syntax incomplete. (C) List the value(s) of x for which f(x) is non-differentiable. Enter your answer as a comma-separated list, if needed (eg. -2, 3, 5).…
A graph of the function f is given below: Study the graph of f at the value given below. Select each of the following that applies for the value a = -4. f is defined at = a. f is not defined at 2 = a. If is continuous at x = a. Of is discontinuous at x = a. Of is smooth at x = a. f is not smooth at x = a. If has a horizontal tangent line at x = a. f has a vertical tangent line at x = a. Of has a oblique/slanted tangent line at x = a. Of has no tangent line at x = a. f(a + h) − f(a) h lim is finite. h→0 f(a + h) - f(a) lim is infinite. h→0 h f(a + h) - f(a) lim does not exist. h→0 h f'(a) is defined. f'(a) is undefined. If is differentiable at x = a. If is not differentiable at x = a.

Chapter 4 Solutions

Calculus

Ch. 4.1 - Prob. 11PSCh. 4.1 - Prob. 12PSCh. 4.1 - Prob. 13PSCh. 4.1 - Prob. 14PSCh. 4.1 - Prob. 15PSCh. 4.1 - Prob. 16PSCh. 4.1 - Prob. 17PSCh. 4.1 - Prob. 18PSCh. 4.1 - Prob. 19PSCh. 4.1 - Prob. 20PSCh. 4.1 - Prob. 21PSCh. 4.1 - Prob. 22PSCh. 4.1 - Prob. 23PSCh. 4.1 - Prob. 24PSCh. 4.1 - Prob. 25PSCh. 4.1 - Prob. 26PSCh. 4.1 - Prob. 27PSCh. 4.1 - Prob. 28PSCh. 4.1 - Prob. 29PSCh. 4.1 - Prob. 30PSCh. 4.1 - Prob. 31PSCh. 4.1 - Prob. 32PSCh. 4.1 - Prob. 33PSCh. 4.1 - Prob. 34PSCh. 4.1 - Prob. 35PSCh. 4.1 - Prob. 36PSCh. 4.1 - Prob. 37PSCh. 4.1 - Prob. 38PSCh. 4.1 - Prob. 39PSCh. 4.1 - Prob. 40PSCh. 4.1 - Prob. 41PSCh. 4.1 - Prob. 42PSCh. 4.1 - Prob. 43PSCh. 4.1 - Prob. 44PSCh. 4.1 - Prob. 45PSCh. 4.1 - Prob. 46PSCh. 4.1 - Prob. 47PSCh. 4.1 - Prob. 48PSCh. 4.1 - Prob. 49PSCh. 4.1 - Prob. 50PSCh. 4.1 - Prob. 51PSCh. 4.1 - Prob. 52PSCh. 4.1 - Prob. 53PSCh. 4.1 - Prob. 54PSCh. 4.1 - Prob. 55PSCh. 4.1 - Prob. 56PSCh. 4.1 - Prob. 57PSCh. 4.1 - Prob. 58PSCh. 4.1 - Prob. 59PSCh. 4.1 - Prob. 60PSCh. 4.2 - 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Prob. 16PSCh. 4.6 - Prob. 17PSCh. 4.6 - Prob. 18PSCh. 4.6 - Prob. 19PSCh. 4.6 - Prob. 20PSCh. 4.6 - Prob. 21PSCh. 4.6 - Prob. 22PSCh. 4.6 - Prob. 23PSCh. 4.6 - Prob. 24PSCh. 4.6 - Prob. 25PSCh. 4.6 - Prob. 26PSCh. 4.6 - Prob. 27PSCh. 4.6 - Prob. 28PSCh. 4.6 - Prob. 29PSCh. 4.6 - Prob. 30PSCh. 4.6 - Prob. 31PSCh. 4.6 - Prob. 32PSCh. 4.6 - Prob. 33PSCh. 4.6 - Prob. 34PSCh. 4.6 - Prob. 35PSCh. 4.6 - Prob. 36PSCh. 4.6 - Prob. 37PSCh. 4.6 - Prob. 38PSCh. 4.6 - Prob. 39PSCh. 4.6 - Prob. 40PSCh. 4.6 - Prob. 41PSCh. 4.6 - Prob. 42PSCh. 4.6 - Prob. 43PSCh. 4.6 - Prob. 44PSCh. 4.6 - Prob. 45PSCh. 4.6 - Prob. 46PSCh. 4.6 - Prob. 47PSCh. 4.6 - Prob. 48PSCh. 4.6 - Prob. 49PSCh. 4.6 - Prob. 50PSCh. 4.6 - Prob. 51PSCh. 4.6 - Prob. 52PSCh. 4.6 - Prob. 53PSCh. 4.6 - Prob. 54PSCh. 4.6 - Prob. 55PSCh. 4.6 - Prob. 56PSCh. 4.6 - Prob. 57PSCh. 4.6 - Prob. 58PSCh. 4.6 - Prob. 59PSCh. 4.6 - Prob. 60PSCh. 4.7 - Prob. 1PSCh. 4.7 - Prob. 2PSCh. 4.7 - Prob. 3PSCh. 4.7 - Prob. 4PSCh. 4.7 - Prob. 5PSCh. 4.7 - Prob. 6PSCh. 4.7 - Prob. 7PSCh. 4.7 - Prob. 8PSCh. 4.7 - Prob. 9PSCh. 4.7 - Prob. 10PSCh. 4.7 - Prob. 11PSCh. 4.7 - Prob. 12PSCh. 4.7 - Prob. 13PSCh. 4.7 - Prob. 14PSCh. 4.7 - Prob. 15PSCh. 4.7 - Prob. 16PSCh. 4.7 - Prob. 17PSCh. 4.7 - Prob. 18PSCh. 4.7 - Prob. 19PSCh. 4.7 - Prob. 20PSCh. 4.7 - Prob. 21PSCh. 4.7 - Prob. 22PSCh. 4.7 - Prob. 23PSCh. 4.7 - Prob. 24PSCh. 4.7 - Prob. 25PSCh. 4.7 - Prob. 26PSCh. 4.7 - Prob. 27PSCh. 4.7 - Prob. 28PSCh. 4.7 - Prob. 29PSCh. 4.7 - Prob. 30PSCh. 4.7 - Prob. 31PSCh. 4.7 - Prob. 32PSCh. 4.7 - Prob. 33PSCh. 4.7 - Prob. 34PSCh. 4.7 - Prob. 35PSCh. 4.7 - Prob. 36PSCh. 4.7 - Prob. 37PSCh. 4.7 - Prob. 38PSCh. 4.7 - Prob. 39PSCh. 4.7 - Prob. 40PSCh. 4.7 - Prob. 41PSCh. 4.7 - Prob. 42PSCh. 4.7 - Prob. 43PSCh. 4.7 - Prob. 44PSCh. 4.7 - Prob. 45PSCh. 4.7 - Prob. 46PSCh. 4.7 - Prob. 47PSCh. 4.7 - Prob. 48PSCh. 4.7 - Prob. 49PSCh. 4.7 - Prob. 50PSCh. 4.7 - Prob. 51PSCh. 4.7 - Prob. 52PSCh. 4.7 - Prob. 53PSCh. 4.7 - Prob. 54PSCh. 4.7 - Prob. 55PSCh. 4.7 - Prob. 56PSCh. 4.7 - Prob. 57PSCh. 4.7 - Prob. 58PSCh. 4.7 - Prob. 59PSCh. 4.7 - Prob. 60PSCh. 4 - Prob. 1PECh. 4 - Prob. 2PECh. 4 - Prob. 3PECh. 4 - Prob. 4PECh. 4 - Prob. 5PECh. 4 - Prob. 6PECh. 4 - Prob. 7PECh. 4 - Prob. 8PECh. 4 - Prob. 9PECh. 4 - Prob. 10PECh. 4 - Prob. 11PECh. 4 - Prob. 12PECh. 4 - Prob. 13PECh. 4 - Prob. 14PECh. 4 - Prob. 15PECh. 4 - Prob. 16PECh. 4 - Prob. 17PECh. 4 - Prob. 18PECh. 4 - Prob. 19PECh. 4 - Prob. 20PECh. 4 - Prob. 21PECh. 4 - Prob. 22PECh. 4 - Prob. 23PECh. 4 - Prob. 24PECh. 4 - Prob. 25PECh. 4 - Prob. 26PECh. 4 - Prob. 27PECh. 4 - Prob. 28PECh. 4 - Prob. 29PECh. 4 - Prob. 30PECh. 4 - Prob. 1SPCh. 4 - Prob. 2SPCh. 4 - Prob. 3SPCh. 4 - Prob. 4SPCh. 4 - Prob. 5SPCh. 4 - Prob. 6SPCh. 4 - Prob. 7SPCh. 4 - Prob. 8SPCh. 4 - Prob. 9SPCh. 4 - Prob. 10SPCh. 4 - Prob. 11SPCh. 4 - Prob. 12SPCh. 4 - Prob. 13SPCh. 4 - Prob. 14SPCh. 4 - Prob. 15SPCh. 4 - Prob. 16SPCh. 4 - Prob. 17SPCh. 4 - Prob. 18SPCh. 4 - Prob. 19SPCh. 4 - Prob. 20SPCh. 4 - Prob. 21SPCh. 4 - Prob. 22SPCh. 4 - Prob. 23SPCh. 4 - Prob. 24SPCh. 4 - 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