Math Is Fun Forum

Joker

Member

Registered: 2010-04-20

Posts: 51

Re: Finding x co-ordinates please help me

oooo found my mistake 6x3=18 not 24 ops

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Finding x co-ordinates please help me

Nope; Don't put the 4 on the left for this, you have

f'(x) = f'(3) = (x -2)2(x+1) + (x-2)^2 = (3-2)^2 + 2(3+1)(3-2) = 1 + 8 = 9

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Joker

Member

Registered: 2010-04-20

Posts: 51

Re: Finding x co-ordinates please help me

ah gotcha

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Finding x co-ordinates please help me

So the slope of f(x) is 9 at the point (3 , 4), we now need to find another point on f(x) that has a tangent with a slope of 9. Yes?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Joker

Member

Registered: 2010-04-20

Posts: 51

Re: Finding x co-ordinates please help me

Am i finding the x co-ordinate of a ponit where the tangent is parallel to another tangent?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Finding x co-ordinates please help me

That's correct on the line y= (x+1)(x-2)^2 there is another point that has a tangent with a slope of 9. Use the derivative to find it.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Joker

Member

Registered: 2010-04-20

Posts: 51

Re: Finding x co-ordinates please help me

do i use y=4 to find the x co-ordinate?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Finding x co-ordinates please help me

Since the derivative is the slope at any point we need to find some point (x,y) that has a slope of 9. So set f'(x) to 9 and solve for the x.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Joker

Member

Registered: 2010-04-20

Posts: 51

Re: Finding x co-ordinates please help me

Something like this?
9 = (x-2)^2 + 2(x+1)(x-2)
9 = x^2-2x-2x+4+2x^2-4x+2x-4
3x^2=6x=9

Joker

Member

Registered: 2010-04-20

Posts: 51

Re: Finding x co-ordinates please help me

3x^2-6x=9

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Finding x co-ordinates please help me

Sorry, that is correct, now solve that quadratic.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Joker

Member

Registered: 2010-04-20

Posts: 51

Re: Finding x co-ordinates please help me

(3x^2+3)(x-3)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Finding x co-ordinates please help me

(3x^2+3)(x-3) That is not quite right. Please check your work.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Joker

Member

Registered: 2010-04-20

Posts: 51

Re: Finding x co-ordinates please help me

ops (3x+3)(x-3)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Finding x co-ordinates please help me

That's good, you are almost done. Solve that by setting it equal to 0.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Joker

Member

Registered: 2010-04-20

Posts: 51

Re: Finding x co-ordinates please help me

like this?
3x+3=0                         x-3=0
x=-1                              x=3

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Finding x co-ordinates please help me

Yes, now you have the 2  x coordinates of your f(x) that have a slope of 9. The x = 3 we have have already got the tangent to. Now just get the other tangent at point (-1,y).

This is done using the slope form of a line. y = m* x + b. You have the slope m = 9 and you have x = -1 you need y and b and you are done.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Joker

Member

Registered: 2010-04-20

Posts: 51

Re: Finding x co-ordinates please help me

how do i find y and b ? plug -1 into the derivative ?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Finding x co-ordinates please help me

To get the y you plug x = -1  into f(x) The original equation, then you solve for b.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Joker

Member

Registered: 2010-04-20

Posts: 51

Re: Finding x co-ordinates please help me

some how i got y=0

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Finding x co-ordinates please help me

Kay - rect !!!!! So the point is (-1,0), Solve y = m* x + b

0 = 9 (-1) + b
9 = b

First tangent y = 9x - 23

second tangent y = 9x + 9

Graph all 3 equations on your graphic calculator and see that they are tangents at the 2 points and that they are parallel.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.