Problem

Estimate the intervals of concavity to one decima…

00:34

Problem 63 Medium Difficulty

Estimate the intervals of concavity to one decimal place by using a computer algebra system to compute and graph $ f" $.

$ f(x) = \frac{x^4 + x^3 + 1}{\sqrt{x^2 + x + 1}} $

Answer

From the graph above, we see that $f(x)$ is
concave upward on $(-\infty,-0.62) \cup(0.02, \infty)$ and
concave downward on $(-0.62,0.02)$

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

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 I've used a computer system to find the second derivative of our original function F of X. And it came out to be this huge, very complicated function. Um Which would have been very hard to find if we didn't use a computer. Um And so now we're just gonna look at the graph which I have here on dez mose. And we're gonna look at what the intervals of con cavity are. So where this is concave up and concave down. Well, we know we're concave up whenever we have positive Y values for our second derivative. So that's going to be from negative infinity. Since it doesn't look to be coming back down anytime soon. To this point here at- .635. And then We go where concave down from negative .635 all the way to this point at .029. And then we're back to being concave up. So The points to remember are negative .635 and negative .029. So if you go back here can say that we are concave up from negative infinity- .635. And from 0.29 to infinity. Since those where we had positive values for our second derivative and we are concave down on the interval of negative point. Did I not put a negative sign up here Should be -635. Um Yeah, so from negative .635 2.029 is where we are con caved out. So these are the two intervals for concave up and concave down. And we found these just using the graph of our second derivative.

Kian M.

Oregon State University

Topics

Derivatives

Differentiation

Volume

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 3

How Derivatives Affect the Shape of a Graph

Problem