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! :).