# Differentiation help

• June 30th 2012, 08:37 PM
kl050196
Differentiation help
The gradient of a curve y= ax^2 +bx at the point (2,4) is -8, calculate the values of a and b
• June 30th 2012, 10:13 PM
richard1234
Re: Differentiation help
$\frac{dy}{dx} = 2ax + b$. Specifically, at (2,4), $\frac{dy}{dx} = 2a(2) + b = 4a + b = -8$.

However...we have one equation, two variables. Can't really find a unique solution (a,b). However, we do know that, for the original equation, when x = 2, y = 4.

$4 = a(2^2) + b(2) = 4a + 2b$, so we have the system

$4a + b = -8$
$4a + 2b = 4$

Solve the system of equations.
• June 30th 2012, 10:13 PM
biffboy
Re: Differentiation help
(2,4) is on curve so 4a+2b=4 Gradient=2ax+b When x=2 gradient=-8 so 4a+b=-8 Solve the simultaneous equations to find a and b