MATH 110 Lecture 24: Intervals
Document Summary
Three clicker questions were done in the beginning of class. A function f is increasing on an interval (a,b) if for any two numbers c and d in f (c)f (d ) (a,b) whenever c >d. If f " (x)>0 for all x in interval (a,b) If f " (x)<0 for all x in interval (a,b) , then f f is increasing on is decreasing on (a,b) While this result is fairly intuitive, its proof requires the mean value theorem, which is f " (x)=0 for all x in interval is constant on (a,b) , then f the most important theorem from differential calculus. The increasing/decreasing behavior of a continuous function is consistent between points where the derivative is equal to zero or undefined.
