Find the value of c guaranteed by the Intermediate Value Theorem. .

Question

Find the value of c guaranteed by the Intermediate Value Theorem.  .

Quizplus · Accepted Answer

The Intermediate Value Theorem states that if a function is continuous on a closed interval [a, b], then for any number k between f(a) and f(b), there is at least one number c between a and b such that f(c) = k. 
In this case, we have a function that is continuous on the interval [1, 7], and we are looking for a value of c such that f(c) = 4. 
From the graph, we can see that f(1) = 2 and f(7) = 6, so by the Intermediate Value Theorem, there must be a value of c between 1 and 7 where f(c) = 4. 
We can eliminate choices A, B, D, and E because they are not values between f(1) and f(7). Therefore, the only possible value for c is 5, which is between f(1) and f(7). Thus, the answer is C.

Find the Value of C Guaranteed by the Intermediate Value