Let [a,b] be a closed and bounded interval, let k∈ℝ, and let f:[a,b]→ℝ be a function. Suppose that f satisfies the conclusion of the intermediate value theorem. Show that the function g(x) defined by g(x) = kf(x) for all x∈[a,b] also satisfies the conclusion of the intermediate value theorem.

Let [a,b] be a closed and bounded interval, let k∈ℝ, and let f:[a,b]→ℝ be a function. Suppose that f satisfies the conclusion of the intermediate value theorem. Show that the function g(x) defined by g(x) = kf(x) for all x∈[a,b] also satisfies the conclusion of the intermediate value theorem.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.CR: Chapter 6 Review

Problem 2CR

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