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.
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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: ...
Your equation must pass through (2,-6) ....
Solve  and  for a and b.
Thanks a lot! Cheers!
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