Critical number & maximum and minimum values  Derivative Applications
Critical number & maximum and minimum values
Another powerful usage of differential calculus is optimization, for example, finding the number of products needed to be sold at a store to maximize its monthly revenue or to minimize its monthly costs. In this section, we will link the application of differential calculus with finding the local extrema, the maxima and minima, of a function.
Lessons
Notes:
critical number: a number$\ c$ in the domain of a function$\ f$ such that:

Intro Lesson
How to describe graphs of functions?

1.
Find the critical numbers of the function:

3.
$f(x)=3x^{5}15x^{4}+25x^{3}15x^{2}+5$