prove using mean value theorem Theorem 4.13. Suppose that f is continuous on the closed interval I and has aderivative at each point of I₁, the interior of I.88f(a)|1a1हूँy = f(x)slope = f'()|f(b)1(a) If f' is positive on I₁, then f is increasing on I.(b) If f' is negative on I₁, then f is decreasing on I.See Figure 4.2.XFigure 4.4. Illustrating the Mean-value theorem.4. Elementary Theory of Differentiation

use the mean value theorem to prove the questions

Theorem 4.13. Suppose that f is continuous on the closed interval I and has a derivative at each point of I₁, the interior of I. 88 f(a)| y = f(x) slope = f'(E) 1 1 | f(b) 1 b (a) If f' is positive on I₁, then f is increasing on I. (b) Iff' is negative on I₁, then f is decreasing on I. X Figure 4.4. Illustrating the Mean-value theorem. 4. Elementary Theory of Differentiation

Theorem 4.13. Suppose that f is continuous on the closed interval I and has a derivative at each point of I₁, the interior of I. 88 f(a)| y = f(x) slope = f'(E) 1 1 | f(b) 1 b (a) If f' is positive on I₁, then f is increasing on I. (b) Iff' is negative on I₁, then f is decreasing on I. X Figure 4.4. Illustrating the Mean-value theorem. 4. Elementary Theory of Differentiation

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.

Chapter5: Graphs And The Derivative

Section5.1: Increasing And Decreasing Functions

Problem 44E: Where is the function defined by f(x)=ex increasing? Decreasing? Where is the tangent line...

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