# Math Help - Cubic Equation

1. ## Cubic Equation

A curve with equation y = ax^3 + bx passes through the origin at an angle of 45 degrees and passes through the point (2,-6)

FInd values a and b.

Not sure how to tackle this question! Thanks.

2. Ange of 45 degrees will mean a gradient of 1

Differentiate to find dy/dx

Know dy/dx = 1 when x = 0

And from given point y = -6 when x = 2

Creates two simultaneous equations which you can solve to find a and b

3. They give you the slope, 45 degrees. That's a slope of 1

Set up your derivative and set it equal to 1 at the origin:

$\frac{d}{dx}[ax^{3}+bx]=3ax^{2}+b$

$3a(0)^{2}+b=1$...[1]

Your equation must pass through (2,-6)

$a(2)^{3}+b(2)=-6$....[2]

Solve [1] and [2] for a and b.

4. Thanks a lot! Cheers!