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Let f(x) = e^x +3x. A student was asked to show why there was a root c in the in

ID: 2865265 • Letter: L

Question

Let f(x) = e^x +3x. A student was asked to show why there was a root c in the interval [1.0,0]. The student responded with the following argument: First we must calculate the value of the function at the end points of the interval. f(1) = e^1 3 and f(0) = 1. Since the function f(x) is negative when x = 1 and positive when x = 0, by the Intermediate Value Theorem there exists a root c in the interval [1.0,0] such that f(c) = 0. This means that f(x) has a root in the interval.

Does the student’s response show that there is a root in the interval?

a. yes

b. no

why?

Explanation / Answer

yes

Exactly as the intermediate value theorem guarantees the existence of a root in that interval.

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