Question

someone please help..

Answer 1

Can you find the equation of the graph?

Answer 2

can you do the whole sum.

Answer 3

May I ask where this question came from? Is it from a book, online assignment? I Just want to find the right chaper, and perhaps question.

Answer 4

its from an e-book.. chapter 2..

Answer 5

First question 18 a). Do you need help from the beginning or do you have some idea?

Answer 6

okay, so the original function is x^3-x^2-2x

Answer 7

i have no idea how to do the 18) a

Answer 8

Now take the derivative of the original function

Answer 9

@zordoloom please stop giving out the answers!

Answer 10

you get 3x^2-2x-2

Answer 11

@calculusfunctions i'll let you take over from here.

Answer 12

Thanks @zordoloom !

Answer 13

Now @zaisha from the graph, let's start with you telling me where the zeros (x-intercepts) of the function are.

Answer 14

-2 and + 2

Answer 15

No, you forgot one of them.

Answer 16

0

Answer 17

Yes, now can you tell me the factors corresponding to these zeros?

Answer 18

i dont know

Answer 19

For example, if the zeros of a function are x = a, x = b, and x = c, then the corresponding factors are (x - a), (x - b), and (x - c). Understand? If yes, then please try again.

Answer 20

(x-(-2), (x-0) and (x-2)

Answer 21

Yes but actually never mind because we don't need to find the equation of the curve in order to find the equation of the tangent. I mean we can but it's not necessary so let's start from scratch.

Answer 22

We are asked not to find the equation of the curve, but rather only the equation of the tangent line. You know that the equation of the line is\[y =mx +b\]in slope-intercept form or\[y -y _{1}=m(x -x _{1})\]in slope-point form. @zaisha which one of these two equations are you more familiar and comfortable with?

Answer 23

y=mx+b

Answer 24

Plus that graph is not relative to question 18 a). I realized this after.

Answer 25

OK so we are told that g'(5) = 4. @zaisha do you know what that signifies?

Answer 26

i think its not even relative to 18) b too.. i am so sorry. didnt read it properly

Answer 27

no

Answer 28

Yes that was misleading but let's carry on.

Answer 29

@zaisha g'(5) = 4 implies that the derivative (slope of the tangent line) at x = 5, is 4. In other words m = 4. This means that we have y = 4x + b. Do you understand?

Answer 30

yes

Answer 31

Good! Now can you tell me what g(5) = -3 means?

Answer 32

g(5) = -3 implies that the derivative at x = 5, is -3. y=-3x+b ??

Answer 33

NO, g'(x) means derivative, not g(x). Please try again!

Answer 34

We already took care of the slope part. Forget about that now. What does g(5) = -3 mean?

Answer 35

i dont know

Answer 36

g(a) = b means that y = b when x = a. Hence once again, what does g(5) = -3 imply?

Answer 37

g(5) =-3 implies that y=-3 when x=5

Answer 38

Correct! Hence we have m = 4, x = 5, and y = -3. Given these values of m, x, and y, what do you have to do next to find the equation of the tangent line?

Answer 39

substitute ??

Answer 40

Yes go ahead!

Answer 41

b=-23 ..

Answer 42

Yes!!

Answer 43

So then what is the equation of the tangent line?

Answer 44

y=mx+b ??

Answer 45

That's the general equation. What is the equation of this line?

Answer 46

We just said that m = 4 and b = -23, correct? So then what is the equation of the line?

Answer 47

y=4x-23

Answer 48

Yes!! Which can also be written as

4x - y - 23 = 0

Understand?

Answer 49

yes

Answer 50

Alright now believe it or not, 18 b) is even easier than 18 a). Do you know what to do?

Answer 51

We're told that the tangent line to the curve y = f(x) at (4, 3) also passes through (2, 0). This implies that the tangent passes through the points (4, 3) and (2, 0). Thus what is the slope of this tangent line? Remember that the slope m of the line passing through the points\[(x _{1}, y _{1}) and (x _{2}, y _{2})\]is given by\[m =\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\]@zaisha what is the slope of this line?

Answer 52

i think there is a mistake .. its (0,2) and not (2,0)

Answer 53

Oh yes, that's right. OK what is the slope of the line passing through (4, 3) and (0, 2)?

Answer 54

m=1/4

Answer 55

Yes!! Remember that f '(c) = d means that the derivative (slope of the tangent) at x = c, is d. Thus f '(4) = ?

Answer 56

x=4

Answer 57

What???

Answer 58

I just told you that f '(c) = d means that the derivative (slope of the tangent) at x = c, is d.

Answer 59

Try again!!

Answer 60

i dont think i know the answer

Answer 61

f'(4)=1/4 ??

Answer 62

@zaisha f '(4) means what is the slope (derivative) at x = 4? Since you found that the slope is m = 1/4, then by definition, f '(4) = 1/4. Please help me understand what level you're at so that I may understand why you're having difficulty grasping the fundamentals? Knowing a little background will give me a better idea as to how I can help you better in the future.

Answer 63

Since we're told that y = f(x) has a tangent at (4, 3), this implies that the curve y = f(x) and the tangent line intersect at the point (4, 3). Thus f(4) = 3.

Answer 64

Therefore f(4) = 3 and f '(4) = 1/4. It is literally that simple.

@zaisha do you understand???

Answer 65

yes

Answer 66

OH Yes sorry, in the midst of typing I didn't see until now that you wrote f '(4) = 1/4. Very Good!

Answer 67

thank you

Answer 68

Great! Please practice and review constantly because practice makes perfect, and review enforces confidence!

Answer 69

i will .. thank you so much