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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\ c in the domain of a function f\ f such that:

  • 1.
    How to describe graphs of functions?
    describe a graph of function, the critical number & maximum and minimum values
  • 2.
    Find the critical numbers of the function:
  • 4.
    f(x)=3x515x4+25x315x2+5f(x)=3x^{5}-15x^{4}+25x^{3}-15x^{2}+5
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Critical number & maximum and minimum values

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