Quick questions I had problems with.. ><

[Ahmad]

At a POI the gradient must change from increasing to decreasing, or decreasing to increasing. For example if you think of a y = x^2, the gradient is always increasing, there are no POIs. y = x^3 decreases from the left towards zero, then increases towards the right (after zero).

If the gradient changes from increasing to decreasing, then the derivative of the gradient must change sign. This is also the second derivative, which changes sign.

If the second derivative changes sign, it must be zero at that point (cross the x-axis). Also, if it changes sign, what does that say about the anti-derivative of the 2nd derivative? It shows that it either has a maximum or minimum, and thus, the sign of the derivative does not change.

[avogarbro]

Do you know if we are required to  manually work out integrals if the question does not say "use calculus"?

[Ahmad]

I'm not sure. I'd guess it just depends on how many marks the question is. If it's something like 4 marks, then you'd probably have to. If it's 2 marks, you could probably get away with setting up integral + using calculator.