Stationary Points?

[Yoda]

say if you're given a function, how do you determine when the graph has no stationary points

[alchemy]

say if you're given a function, how do you determine when the graph has no stationary points

If there are no points or solutions where the derivative equals to zero, then that means there's no stationary points.

[Yoda]

but lets say for the function y=ax^3+bx^2+cx+d

[Shadaura]

but lets say for the function y=ax^3+bx^2+cx+d

differentiate it, and make it equal 0. If there is no solution there are no stationary points.

[Zealous]

The best way to find values of this is using the discriminant in the quadratic formula (b^2 - 4ac). If the discriminant is less than 0 there is no solution. (Think about the quadratic formula - b^2 - 4ac is under a square root sign, so if it's less than zero, it cannot exist in VCE methods.

So 4b^2 - 4 * 3a * c < 0

i.e. 4b^2 - 12ac < 0
4b^2 < 12ac
b^2 < 3ac

Any values for a, b and c that fit this criteria will result in the graph having no stationary points.

I see some VCAA 2013 Exam 2 MCQ21 going on there - it was a good question =p.

[IndefatigableLover]

I see some VCAA 2013 Exam 2 MCQ21 going on there - it was a good question =p.

Geez I just looked up the question on the Examiner's Report and only 29% of people got that right :|