Problem

(a) Sketch the graph of the function $ f(x) = x |…

07:25

Problem 60 Hard Difficulty

Where is the greatest integer function $ f(x) = [ x ] $ not differentiable? Find a formula for $ f' $ and sketch its graph.

Name: where is the greatest integer function fx x not differentiable find a formula for f and sketch its g
Uploaded: 2021-08-25
Channel: Numerade
Description: Where is the greatest integer function $ f(x) = [ x ] $ not differentiable? Find a formula for $ f' $ and sketch its graph.

Answer

See step for answer

Discussion

You must be signed in to discuss.

Top Calculus 1 / AB Educators

Anna Marie V.

Campbell University

Heather Z.

Oregon State University

Samuel H.

University of Nottingham

Joseph L.

Boston College

Watch More Solved Questions in Chapter 2

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

Video Transcript

let's talk about this question. It seems that where is the greatest indigent function? Not the friendship. So in the best way to answer this is by drawing the graph of the greatest indigent function. This is the coordinate access. And I'm gonna just brought up the indigenous here. So this is zero one, two, three and so on. Uh this is -1 -2 -3 -4 and so on. Over here we have one, two, 34. Uh and over here we have -1 -2 and so on. So between 0-1, between 0-1, The functional value of zero From 1 to 2, The functional value is one from 2 to 3. From 2 to 3. The functional value is two and so on. From -1-0, There's zero. The open circle means the start improving values -1 From -2 to -1, the values -2 and so on. Clearly we can see that it has a jump discontinuity at each integral value at each integral value. It has a jump kind of discontinuity so it is not differentiable at all those points. So we're going to say that it is not differentiate able at all integral whites. And saying that find the formula for the f dash and sketches craft clearly the derivative whatever the function and this function is always a constant because function between uh function between 0 to 10 function between 1 to 2 as one function between 2 to 3 uh is two and so on. Uh So wherever the functional value it gets a functional value that's a constant. Because function is uh let's call it minus two for x. Between minus two to minus one, it's minus one for x. Between minus one and 00 for X between 10 and one. It's one for X, between one and two and so on. So whenever we will take the derivative the derivative of a constant is always zero. So we're gonna see that if dash X is always zero, definitely excluding the integral points because that's where the function is different. She able and if we have to draw the graph of uh Everyday Acts Equal to zero. So why equal to zero is just the X. Axis Except the integral value. So this is how it's gonna graph is gonna look like. So we'll just make a draw the plot the integral values and we're gonna draw holes over here. So that is a whole this is a whole, this is a whole, this is a whole and so on. This is how the graph of F dash X is going to look like because F dash X is always zero. Thank you

Darshan M.

NIT Bhopal

Topics

Limits

Derivatives

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 8

The Derivative as a Function