Suppose that f (x) is defined and continuous for all real number x and assume that f (x) takes on...

Question:

Suppose that {eq}f (x) {/eq} is defined and continuous for all real number {eq}x {/eq} and assume that {eq}f (x) {/eq} takes on the following values: {eq}\displaystyle f (-2) = 6,\ f (0)= -3,\ f (2) = 4,\ f (3) = 0,\ f (4) = -1,\ f (7)= -3,\ \text{and}\ f (10) = 8 {/eq}. Give a list of non overlapping intervals in which solutions to the equation {eq}f (x) = 0 {/eq} can be found.

Intermediate Value Theorem

We can draw a number of conclusions about a function if we know that it is continuous. One of these conclusions is stated in the Intermediate Value Theorem. This theorem states that if we know what a continuous function equals at the endpoints of an interval, we know that the function must equal every value in between these points at least once.

Answer and Explanation:

Since this function is defined to be continuous, we know that we can apply the Intermediate Value Theorem to it. One application of this theorem is...

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Intermediate Value Theorem: Definition

from Math 104: Calculus

Chapter 2 / Lesson 4
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