Question

Suppose f(x) is a differentiable function with
f(1)=2, f(2)=-2, f'(2)=3,f'(1)=5 and f(5)=1

State an equation of a line is a tangent to the graph of f.

Answer 1

Assume the tangent line is y' = mx + b then

5 = m + b
3 = 2m + b

so m = -2 and b = 7.

y' = -2x + 7

Answer 2

Did you have to use f'(1)=5 to find the answer?

Answer 3

5 = m + b uses f'(1)=5
3 = 2m + b uses f'(2)=3

I assume there is other parts to the question that u need the other data for (eg u can find the curve).

Answer 4

Hmm this is the whole question.There is no other part.
So for f'(1)=5 is using coordinate (1,5)
Then for f(1)=2 is using coordinate (2,1)?

Answer 5

So for f'(1)=5 is using coordinate (1,5)-- I used this one.
Then for f(1)=2 is using coordinate (2,1)? I didn't use this one, if you are going to use it for something, f(1) means "the value of the function when x is 1 ie the x value) and 2 is the result or y value.

Answer 6

What is the difference for both of this? since both y value are positioned at the right side of the equation.

Answer 7

I don't understand your question.

The difference of what?

Answer 8

f(x) and f'(x)

Answer 9

The first one means "function of x" and the second one is another way of writing dy/dx (the derivative).

Answer 10

So how to do you know f'(1)=5 is using the cordinate (1,5) instead of (5,1)?

Answer 11

Same like the other, it means the value of the derivative when x is 1 is 5 (ie the y value).

Answer 12

Let me show u in a more concrete way....

Answer 13

Oh i see.Thanks !!
btw do you know what is the difference between f'(x) and f\[^{-1}\](x) ?

Answer 14

[f ^{-1}(x)\]

Answer 15

sorry typo.
\[f^{-1}(x)\]

Answer 16

Does that clarify things a bit?

Answer 17

Hmm yea a little.thanks!

Answer 18

f^-1 (f(x)) = x It is the inverse function, which reverses the action of a function.

Answer 19

hmm thanks!! may i know how you draw the graph?

Answer 20

Paint accessory.

Answer 21

cool thanks alot!!

Answer 22

ur welcome.

Answer 23

Hmm there is no answer in the choice given.

Answer 24

?

Answer 25

Sorry, what do u say?

Answer 26

hmm the answer u gave me is not in the choice given.
The choice given :
(a) y-3 = 2(x-1)
(b) y-2=x-1
(c) y-2=5(x-1)
(d) y+4=5(x-2)
(e) y-4=5(x-2)

Answer 27

I don't know what to tell u, my equation satisfies

f'(2)=3,f'(1)=5 (ie if you substitute the values in, it equates)

Let me try subbing the values in the equations above.

Answer 28

Hmm okay.:)

Answer 29

None of the equations given in your choices satisfy both of the conditions.

Either the question is wrong or the answers are.

Answer 30

Yea.thats the problem and there is no suggested answer for it.

Answer 31

Are u sure both of these are right?

f'(2)=3,f'(1)=5

Answer 32

Note the dash after the f.

Answer 33

Yes.double checked.

Answer 34

k, let me check my working again...

Answer 35

Okay.Thanks again!!

Answer 36

I stand by my answer if that is the question.

What I don't understand is why they have given you the extra pieces of information that u don't need for anything (apparently).

Answer 37

yes i am kind of condused with the question too.thanks btw:)

Answer 38

Where is the question from?

Answer 39

hmm a maths placement test from a university in hong kong.

Answer 40

I asked on the main board for someone to come check me...

Answer 41

okay thanks alot!!

Answer 42

it would appear that you need to find a function that matches the information?

f(1)=2 f'(1)=5
f(2)=-2 f'(2)=3
f(5)=1

Answer 43

Yes, that's the way I read it, can't see why u need the f info though

(Mind u quite a few things I don't see these days:-)

Answer 44

Well, they asked for a tangent line..

Answer 45

I assumed it didn't matter, they wanted a line so I used the f' info.

Answer 46

k so can I post the link

http://openstudy.com/groups/mathematics/updates/4e2ec4e60b8bd8322c635ff5

Answer 47

f(x) = ax^2 +bx + c ; f'(x) = 2ax + b

f'(1) = 2(1)a + b = 5
f'(2) = 2(2)a + b = 3

2a + b = 5 ; *-1
4a + b = 3

-2a -b = -5
4a +b = 3
-----------
2a = -2

a = -1
............................
4(-1) + b = 3

b = 7
.......................

this look right so far?

Answer 48

That's what I got.

Answer 49

good; then lets see where this takes me :)

f(1) = -(1)^2 +7(1) +c = 2
-1 + 7 + c = 2
c = -4

f(2) = -(2)^2 + 7(2) + c = -2
-4 + 14 + c = -2
c = -12 ... hmm, try that like this then

f(1) = (-1)^2 + 7(1) + c = 2
1 + 7 + c = 2
c = -6

f(2) = (-2)^2 + 7(2) + c = -2
4 + 14 + c = -2
c = -20 .... it might not be quadratic ???

Answer 50

this might help....

given the points (1,2) (2,-2) and (5,1);

the slope at (1,2) = 5
the slope at (2,-2) = 3

the equation of the tangent line is:

y-Py = m(x-Px) to wit:

y-2 = 5(x-1)
y+2 = 3(x-2)

from your answer choices tho:

(a) y-3 = 2(x-1)
(b) y-2=x-1
(c) y-2=5(x-1) <-- this matches
(d) y+4=5(x-2)
(e) y-4=5(x-2)

Answer 51

Hmm how do you get the slope at (1,2) and (2,-2)?

Answer 52

How does c match f'(2) = 3?

Answer 53

the question is simply asking for which answer agrees with any of the information presented.

f'(x) IS slope, so we have to use the information given and adapt it to fit the answers

Answer 54

Or even f'(1) = 5

Answer 55

f'x is not slope...

Answer 56

f'(x) defines the slope of the line at a given point ...

Answer 57

f'x is a line

Answer 58

f'(1) = 5 means that the slope of the tangent line at f(1) IS 5

Answer 59

I read it as tangent line with slope as derivative...duh!

Answer 60

:)

Answer 61

thanks alot!!

Answer 62

youre welcome; once I saw the answer choices it made more sense of what we needed to do ...