Use the first and second derivatives of the function y = x^3-3x^2-9x+15 to find the intervals of increase and decrease. Help!?
The function is decreasing for
You may benefit from looking at some videos where the derivatives are explained, for instance
It is always a good idea to start with drawing a graph of your 3rd degree function (I've used Geogebra):
The graph shows that for
Let's use the 1st and 2nd derivatives to find this, as requested in the task:
The first derivative
We see that
Next: the 2nd derivative
A negative value tells us that the slope is changing from an increase to decrease
A positive value tells us that the slope is changing from a decrease to increase.
This is actually in agreement with what we could see from the graph.