Question

If f(x) is continuous on [1,4] and f(10)=3, f(4)=3 and k=15, then which statement(s) would be true regarding a c value in [1,4] where f(c)=15? PLEASE HELP WILL REWARD BRANLIEST!

Answer 1

The intermediate value theorem says that, for a function $f(x)$ continuous on the closed interval $[a,b]$, there is at least one $c$ on the open interval $(a,b)$ such that either $f(a)\le f(c)\le f(b)$ or $f(b)\le f(c)\le f(a)$. Basically, if you know the values of the function at the endpoints of some interval, we can only guarantee the function takes on a value between the values at the endpoints.

In this case, we're told $f$ is continuous on [1, 4], and $f(1)>f(4)$. By the IVT, we know there is some $c$ in (1, 4) such that $3\le f(c)\le10$. We don't know for sure that $f$ takes on a value of 15 in this interval. So the answer is A.