True or false: increasing and decreasing

Exercise and reference answers

Questions

1. Statement is true

   Yes

   Statement

   f is increasing on (a,b) if x₁ < x₂ implies f(x₁) < f(x₂) there.

2. Statement is true

   Yes

   Statement

   f ′(x) ≥ 0 on an interval indicates f is increasing there.

3. Statement is true

   No

   Statement

   f is decreasing when x₁ < x₂ implies f(x₁) < f(x₂).

4. Statement is true

   Yes

   Statement

   A constant function has f(x) = c throughout the interval.

5. Statement is true

   No

   Statement

   A constant function is strictly increasing.

Explanation