The gradient of a curve y= ax^2 +bx at the point (2,4) is -8, calculate the values of a and b

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- Jun 30th 2012, 08:37 PMkl050196Differentiation help
The gradient of a curve y= ax^2 +bx at the point (2,4) is -8, calculate the values of a and b

- Jun 30th 2012, 10:13 PMrichard1234Re: Differentiation help
$\displaystyle \frac{dy}{dx} = 2ax + b$. Specifically, at (2,4), $\displaystyle \frac{dy}{dx} = 2a(2) + b = 4a + b = -8$.

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.

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

$\displaystyle 4a + b = -8$

$\displaystyle 4a + 2b = 4$

Solve the system of equations. - Jun 30th 2012, 10:13 PMbiffboyRe: 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