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Mean Value Theorem
Answered
Adrianna Macias
2022-07-16
Explain in your own words what the Intermediate Value Theorem says and why it seems plausible.
.A.
The Intermediate Value Theorem states that for a continuous function f(x) over the closed interval [a,b], f(x) takes on every value between f(a) and f(b). This seems plausible because if the function did not take on every value between f(a) and f(b), there would be a value for f(x) that did not exist, and thus the function would not be continuous.
B
The Intermediate Value Theorem states that for every value of x between a and b in f(x), if f(a) exists, then f(b) must exist if b is in the domain. This seems plausible because if the function did not take on every value between f(a) and f(b), there would be a value for f(x) that did not exist, and thus the function would not be continuous.
C.
The Intermediate Value Theorem states that for a continuous function f(x) over the closed interval [a,b], f(x) takes on every value between f(a) and f(b). This seems plausible because if b is in the domain of x, then f(b) must exist.
D.
The Intermediate Value Theorem states that for every value of x between a and b in f(x), if f(a) exists, then f(b) must exist if b is in the domain. This seems plausible because if b is in the domain of x, then f(b) must exist.
