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.
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:
$\displaystyle \frac{d}{dx}[ax^{3}+bx]=3ax^{2}+b$
$\displaystyle 3a(0)^{2}+b=1$...[1]
Your equation must pass through (2,-6)
$\displaystyle a(2)^{3}+b(2)=-6$....[2]
Solve [1] and [2] for a and b.