Find a point given a derivative and a point.

[Qube]

Homework Statement

http://i2.minus.com/jyK7QefQtK8Ul.png

Homework Equations

Point-slope form of a line.

y - y1 = m(x - x1)

The Attempt at a Solution

I'm assuming this is the correct approach to this problem (see below):

http://i4.minus.com/ibnDPl1kiE2f6p.jpg

 

[Saitama]

The question requires you to solve the differential equation f'(x)=2-4/sqrt(x). What you are calculating is the tangent line at any point.

 

[Qube]

https://scontent-b-mia.xx.fbcdn.net/hphotos-prn2/v/1394798_10200979928602153_16381899_n.jpg?oh=ad0bd782b9aac7d121813066be119b79&oe=5275B635

Solving the differential ... is this what you mean?

 

[Saitama]

<image>

Solving the differential ... is this what you mean?

What you just did doesn't make any sense. Even if you haven't yet learned solving the differential equations, this one isn't really hard.

You have dy=(2-4/sqrt(x))dx. You simply need to integrate both the sides.

 

[Qube]

Alright, I integrate and I get y = 2x - (8)x^(1/2)

This is odd since I don't think we've learned integration yet. I know it, but ...

I suppose y = 8 - 8(2) = -8?

 

[Qube]

What you just did doesn't make any sense. Even if you haven't yet learned solving the differential equations, this one isn't really hard.

You have dy=(2-4/sqrt(x))dx. You simply need to integrate both the sides.

What I did I think was linearization and I found the change in y (dy). Knowing how much y changed from the original y-coordinate of the point can help me find the new y.

I think. I'm waiting to be either corrected or affirmed.

 

[Saitama]

Alright, I integrate and I get y = 2x - (8)x^(1/2)

Almost but you missed the constant of integration. You need to use the given information to find the constant.

 

[Mark44]

Alright, I integrate and I get y = 2x - (8)x^(1/2)

This is odd since I don't think we've learned integration yet. I know it, but ...

I suppose y = 8 - 8(2) = -8?

When you integrate, you also get the constant of integration, so you should have y = f(x) = 2x - 8√x + C. You're given that the point (1, -2) is on the graph of f, so you can solve for C.

 

[Qube]

Oh good point. The constant should be 4.

-2 = 2 - 8(1) + c = -6 + c.

So my original answer is off by 4. The answer I suppose is -4? C?

 

[Saitama]

Oh good point. The constant should be 4.

-2 = 2 - 8(1) + c = -6 + c.

So my original answer is off by 4. The answer I suppose is -4? C?

No. You are still not done. Now that you have found the constant, write f(x) and evaluate f(4).

EDIT: Yes, the answer is -4, that's what I get.

 

[Qube]

No. You are still not done. Now that you have found the constant, write f(x) and evaluate f(4).

Yes, and it's -4.

y = 2(4) - 8(2) + 4 = 8 - 16 + 4 and that's -8 plus 4 = -4.

Thanks guys for reminding me about integration! I c now! :).