# Find a point given a derivative and a point.

1. Nov 1, 2013

### Qube

1. The problem statement, all variables and given/known data

http://i2.minus.com/jyK7QefQtK8Ul.png [Broken]

2. Relevant equations

Point-slope form of a line.

y - y1 = m(x - x1)

3. The attempt at a solution

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

http://i4.minus.com/ibnDPl1kiE2f6p.jpg [Broken]

Last edited by a moderator: May 6, 2017
2. Nov 1, 2013

### 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.

3. Nov 1, 2013

### Qube

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

4. Nov 1, 2013

### Saitama

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.

5. Nov 1, 2013

### 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?

6. Nov 1, 2013

### Qube

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.

7. Nov 1, 2013

### Saitama

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

8. Nov 1, 2013

### Staff: Mentor

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.

9. Nov 1, 2013

### 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?

10. Nov 1, 2013

### Saitama

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.

11. Nov 1, 2013

### Qube

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! :).