4.1 Example in finding the critical numbers of a function:

f(x) = 5+6x-2x Original Equation

(x) = 0+6-6x First derivative

0 = 6-6x Set first derivate equal to zero

6x = 6 simplified

x= 1 simplified

x = 1 solution equals the critical numbers of the function

4.1 Using critical numbers to find max and min

Max is at f(3)

Min is at f(1)

4.1

Absolute maximum at (7,5)

Absolute minimum at (1,0)