Recent questions in Mean Value Theorem

Mean Value Theorem
Answered

Adrianna Macias
2022-07-16

.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.