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.

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

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:



...[1]

Your equation must pass through (2,-6)

....[2]

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

Thanks a lot! Cheers!