Let f be a 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 ?
a. f is increasing on the interval [-2,3], where f(-2)=0 and f(3)=20
b. f is increasing on the interval [-2,3], where f(-2)=15 and f(3)=30
c. f is continuous on the interval [-2,3], where f(-2)=0 and f(3)=20
d. f is continuous on the interval [-2,3], where f(-2)=15 and f(3)=30