# Differentiation help ,

## Homework Statement

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?

## The Attempt at a Solution

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

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

Mark44
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.

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

are these two equations correct..

$$4a + b = 4$$

$$4a + b = 8$$

?

danago
Gold Member
Have another look at the first equation.

Have another look at the first equation.
x=2 so 2x2=4? can you give more hints, cause I am really stuck

thank you!

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

Mark44
Mentor
is it meant to be $$32a + b =4$$ ?
No.

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