Problem

Sketch the graph of a function that satisfies all…

02:00

Question

Answered step-by-step

Problem 24 Easy Difficulty

Sketch the graph of a function that satisfies all of the given conditions

(a) $ f'(x) < 0 $ and $ f"(x) < 0 $ for all $ x $
(b) $ f'(x) > 0 $ and $ f"(x) > 0 $ for all $ x $

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Kian Manafi

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Watch More Solved Questions in Chapter 4

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Problem 75

Problem 76

Problem 77

Problem 78

Problem 79

Problem 80

Problem 81

Problem 82

Problem 83

Problem 84

Problem 85

Problem 86

Problem 87

Problem 88

Problem 89

Problem 90

Problem 91

Problem 92

Problem 93

Video Transcript

So we're told in part a that the derivative of our function F. Of X is less than zero. And also the second derivative of our function F. Of X is less than zero for all X. And what we want to do is use this information to try and sketch a potential graph of this function. And so what this tells us since our first derivative is less than zero for all X. That means that we're decreasing for the entirety of our function. So we're decreasing the entirety of our function. And since we know that the second derivative effects is less than zero, we also know that we are concave down for the entirety of our functions. The second derivative tells us about con cavity in the first derivative tells us about the slope or whether we're increasing or decreasing. And so what we want to do is we want to draw a graph that is both concave down and decreasing for all of its domain. So how we do this is I'm just going to start here and make sure and make sure that we're concave down and we're decreasing this entirety of this curve and then just put an air over there and an arrow like that where we're never actually going to get a horizontal um assume toad or slope or anything like that. We're just going to be concave down this entire way, but we're also decreasing. So this is what a sketch of the graph given these conditions would look like. And for part B we're told that F prime of X is greater than zero and F double prime of X is also greater than zero for all of the X. So in this case we're going to be concave up and increasing for the entirety of our function. So we want to draw a graph that is both concave up. Actually. Drawed on this type of graph that is concave up and increasing for the entirety of the function. So I'm just going to kind of start like like this and go like that and make sure that we're concave up so were curved upwards like a U. Shaped A upwards you shape. And we're also increasing for the entirety of our function. So a graph like this could be a potential sketch for a function given these conditions.

Get More Help with this Textbook

James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups

Study with other students and unlock Numerade solutions for free.

Problem