Question

I have a question in regards to number 6

Answer 1

@precal

Answer 2

What book is this from?

Answer 3

Calculus: Graphical, Numerical, Algebraic

Answer 4

What page?

Answer 5

114

Answer 6

A. All points in [-2,3] B) none c) none

Answer 7

Yes

Answer 8

I know the answer, but idk why

Answer 9

btw not my favorite book
so just like dumb cow said, yes you can take the derivative of the entire graph

Answer 10

Well give it a week or so, some math concepts need to be developed and this is one of them

Answer 11

Lol we move so quickly that we can't

Answer 12

Im in BC

Answer 13

still Calculus is a journey

Answer 14

@amistre64

Answer 15

is it a long question? i cant open the attachment

Answer 16

Well it involves a graph

Answer 17

can you get a screenshot? or a pic?

Answer 18

I can try to draw it

Answer 19

that might work :)

Answer 20

Ok

Answer 21

you draw nice lol

Answer 22

xD

Answer 23

now, it asking by looking at the graph for 3 conditions that may fit. right?

Answer 24

Yes

Answer 25

tell me what your ideas for the defnition of coninuity, and differentiability are.

Answer 26

typos not withstanding of course

Answer 27

Well my book kind of says a continuous function is one that can be drawn in one stroke, without lifting the pencil up. Its hard for me to explain. It says for a function to be differentiable at a point x means that it has a derivative at x

Answer 28

and problem 6, can it be drawn without lifting a pencil?

Answer 29

Yes

Answer 30

But that is only for continuity. Idk how to determine if it is differentiable at its endpoints

Answer 31

That was my big question

Answer 32

picture 2 ants, with rulers glued to their backs ... crawling along the curve

one starts at one end, the other at other end.

Answer 33

the rulers define the slope of the curve at any point that an ant is at.

if there is any point that the ants can approach and meet at, such that the slope shown is the same, then its differentiable .... if thier slopes are not the same, then its not.

Answer 34

does that make any sense?

Answer 35

Yes. The endpoints.

Answer 36

the end points are where the ants would start at. now, if one ant doesnt move, and the other ant walks to the other end of the curve, the slopes of both ants are equal. an endpoint can only be defined by a one sided limit. but this may be author specific

Answer 37

in general, smooth flowing curves are differentiable. things with corners and cusps, and broken lines are not

Answer 38

So as long as the endpoints are continuous, it is differentiable there?

Answer 39

differentiable has to do with limits, and limits dont care about if a point exists or not.

Answer 40

think of limits like a map, the map tells you to cross the bridge, but when you look ahead of you on the real road ... the bridge is out.

Answer 41

the limit is where the bridge would be, regardless of if there is a brdige actually there or not

Answer 42

Ok, so how do you know if it is differentiable with a one sided limit?

Answer 43

you reach the end of your domain, therefore the limit can only be one sided.

Answer 44

Ok, so how would I do it in this example?

Answer 45

Like how do you set that up? How of you know if it is differentiable or not based on the limit?

Answer 46

the walking ants is the best way i know to describe it without delving into any mathing of a function that is not 'defined'

Answer 47

5 and 6 are the same 'type' of problem

Answer 48

I know. I didn't know why 5 was differential at its endpoints either.

Answer 49

notice that in number 5, the slope of the line is the same regardless of where you are at

Answer 50

as you get closer and closer to an endpoint, can you tell what the slope of the line is?

Answer 51

Yes

Answer 52

But that is always the case

Answer 53

for endpoints, yes

Answer 54

the issue is when we are in between the end points

Answer 55

So a function is always differential at its endpoints?

Answer 56

a graph with a limited domain has distinct ends, and as such is always differentiable at the endpoints.

Answer 57

Ok, so as long as it has a restricted domain, and doesn't have any discontinuities it is differential at its endpoints?

Answer 58

limits must be the same when approached from all possible directions/paths.

an endpoint of a curve has only one path, agreed?

Answer 59

Yes. A one sided limit

Answer 60

one sided because thats the only way to get there ....

Answer 61

right

Answer 62

lets take a function x/x^2, from 0<x<3

are we differentiable at the end points?

Answer 63

err, lets do x^2/x instead lol

Answer 64

lol. I have no idea