How do I calculate where a function is increasing/decreasing?
This depends entirely on the gradient of the function, which is calculated as (dy/dx).
At (dy/dx)= 0, the function is neither increasing nor decreasing, since the gradient is zero. The max number of stationary points will be the same as the highest power (of the differential).
Plug in values either side of these stationary points. A positive dy/dx value means that the function is increasing, and a negative one means that the function is decreasing.
For example, say an equation has a stationary point (dy/dx = 0) at x=1. I would try values such as x = 1.1 and x= 0.9. If dy/dx is positive both sides, the function therefore is increasing at x>1 and x<1.
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