# Differentiation equation curve

1. Oct 17, 2007

### Trail_Builder

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

A curve has equation $$y = Ax^3 + Bx^2 + Cx + D$$, where A, B, C and D are constants.
Given that the curve has gradient -4 at the point (1,2) and gradient 8 at the point (-1,6), find A, B, C and D.

2. Relevant equations

3. The attempt at a solution

$$y = Ax^3 + Bx^2 + Cx + D$$
$$dy/dx = 3Ax^2 + 2Bx + C$$
$$-4 = 3A + 2B + C$$ (1)
$$8 = 3A - 2B + C$$ (2)
$$-12 = 4B$$(3) = (1)-(2)
$$B = -3$$

Right here is where I get stuck. If i eliminate A or C, they both go at the same time :S. I think I'm missing a trick here or something.

hope you can help

thanks

Last edited by a moderator: Jul 9, 2014
2. Oct 17, 2007

### Hurkyl

Staff Emeritus
Is there any information in the problem you haven't used?

3. Oct 17, 2007

### Trail_Builder

o wait, do i like substitute the y values in from the co-ordinates given?

4. Oct 17, 2007

### Trail_Builder

right, did that, now i have D and B, but still cant get to the A and C because they always seem to cancel each other out when i stick them in simeltaneous equations :S

ahhh

5. Oct 17, 2007

### Hurkyl

Staff Emeritus
Maybe you're accidentally using the same equations twice? Now that you know B and D, try starting over and use all four equations again. (But plug in the known values for B and D)