MAT 1300 Lecture 10: MAT1300applicationofderivative

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1300
• Professor: Termeh Kousha

Document Summary

A function, f (x), is increasing on the interval (a, b) if for every x1, x2 (a, b) where x1 < x2 we have that f (x1) f (x2). A function, f (x), is decreasing on the interval (a, b) if for every x1, x2 (a, b) where x1 < x2 we have that f (x1) f (x2). Ex: f (x) = 1 x is decreasing on ( , 0) and (0, , f (x) = x2 is decreasing on ( , 0) and increasing on (0, , f (x) = ln(x) is increasing on (0, ) Use the test for intervals of increase and decrease to examine the following functions. (a) f (x) = x2 4 (b) f (x) = x3. A real number a is a critical number of a function, f (x), if a is in the domain of f (x) and either: f (a) does not exist, or, f (a) = 0.