Content
Applications of the First Derivative
Increasing and decreasing intervals, stationary points (maxima and minima), and optimisation
Increasing and decreasing intervals, stationary points (maxima and minima), and optimisation
No exercises available for this concept.
Stationary points are often local extrema.
If f′(a)=0, f is decreasing to the left of a (f′(x)<0), and f is increasing to the right of a (f′(x)>0), then (a,f(a)) is a local minimum.
If f′(a)=0, f is increasing to the left of a (f′(x)<0), and f is decreasing to the right of a (f′(x)>0), then (a,f(a)) is a local maximum.
Powered by Desmos
Optimisation problems require you to find a minimum or maximum value by producing a function f(x), taking its derivative, solving f′(x)=0, and confirming which stationary point(s) are minima or maxima.