Let f be the function of x. Which of the following statements, if true, would guarantee that there is a number c in the interval [-2,3] such that f(c) = 10

Question

1) f is increasing on the interval [-2,3], where f(-2)=0 and f(3)=20

2) f is increasing on the interval [-2,3], where f(-2)=15 and f(3)=30

3) f is continuous on the interval [-2,3], where f(-2)=0 and f(3)=20

4) f is continuous on the interval [-2,3], where f(-2)=15 and f(3)=30

Thank you in advance!

Answer 1

3

You need continuity and that 10 is in the interval between the function values at the endpoints.