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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