Properties of Increasing Functions
Consider the following three statements: I. A function is increasing on an interval if for any values and in the interval, implies . II. If a function is increasing and differentiable on an interval, its derivative is positive on that interval. III. If a function has a positive average rate of change over an interval, the function must be increasing on that interval. Which of the statements is or are true?
A
Only statements I and III are true.
B
Only statements I and II are true.
C
All statements are true.
D
Only statement I is true.
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