let f be a function that is continuous on the closed interval [2,4] with f(2)=10 and f(4)=20. Which of the following is guaranteed by the intermediate value theorem?

Question

let f be a function that is continuous on the closed interval [2,4] with f(2)=10 and f(4)=20. Which of the following is guaranteed by the intermediate value theorem?

a) f(X)=13 has at least one solution in the open interval(2,4)

b)f(3)=15

c)f attains a maximum on the open interval (2,4)

d)f(X)=10 at some other value(s) of x other than x=2

please show works

Answer 1

The only conclusion we can make from the intermediate value theorem is a. For b, c and d the intermediate value theorem is not sufficient.