let f be a function that is continuous on the closed interval [1,3] with f(1)=10 and f(3)=18. which of the following statements must be true?

Question

let f be a function that is continuous on the closed interval [1,3] with f(1)=10 and f(3)=18. which of the following statements must be true?

a) 10≤f(2)≤18

b) f is increasing on the interval [1,3]

c) f(x)=17 has at least one solution in the interval [1,3]

d) f(2)=14

please show works

Answer 1

There are no "works"...c is true because of the intermediate value theorem.