Thread: 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

. Specifically, at (2,4), .

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.

, so we have the system





Solve the system of equations.

(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