# Differentiation help ,

1. Feb 25, 2009

### tweety1234

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

The curve $$y = ax^{2} + bx$$ passes through the point (2,4) with gradient 8. Find a and b .

I have no idea how to work out a and b , do I use simultaneous equations?

2. Relevant equations

3. The attempt at a solution

I have no idea how to work out a and b , do I use simultaneous equations?

2. Feb 25, 2009

### RoryP

3. Feb 25, 2009

### tweety1234

okay so dy/dx = $$2ax + b$$ from this how do I find what a and b equal ?

4. Feb 26, 2009

### Staff: Mentor

Use the fact that (2, 4) is a point on the curve in your given equation, which will give you an equation that involves only a and b.

Then use the fact that at x = 2, dy/dx = 8 in your equation for the derivative. This will give you another equation in a and b.

Finally, solve the two equations in a and b simultaneously.

5. Feb 26, 2009

### tweety1234

so I just sub in the values for x and y ?

are these two equations correct..

$$4a + b = 4$$

$$4a + b = 8$$

?

6. Feb 26, 2009

### danago

Have another look at the first equation.

7. Feb 26, 2009

### tweety1234

x=2 so 2x2=4? can you give more hints, cause I am really stuck

thank you!

8. Feb 26, 2009

### tweety1234

is it meant to be $$32a + b =4$$ ?

9. Feb 26, 2009

### Staff: Mentor

No.

Substitute 2 for x and 4 for y in that equation. The other equation you wrote, 4a + b = 8, is correct.

10. Feb 26, 2009

### tweety1234

$$y = ax^{2} + bx$$ , $$4a + 2b = 4$$ is this correct? so a = 3 and b = -4 ?

11. Feb 26, 2009

### HallsofIvy

Staff Emeritus
Check it yourself. IF a= 3 and b= -4, you have y= 3x2- 4x. What is y when x= 2? What is y' when x= 2?