The graph of the first derivative of a function is shown a) How can we know in which intervals the function f (x) is increasing and where it is decreasing? b) From f´ (x), how can we identify at what values of x, f (x) has a relative maximum or minimum?

The graph of the first derivative of a function is shown a) How can we know in which intervals the function f (x) is increasing and where it is decreasing? b) From f´ (x), how can we identify at what values of x, f (x) has a relative maximum or minimum?

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.

Chapter4: Calculating The Derivative

Section4.3: The Chain Rule

Problem 6YT

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Question

The graph of the first derivative of a function is shown

a) How can we know in which intervals the function f (x) is increasing and where it is decreasing?

b) From f´ (x), how can we identify at what values of x, f (x) has a relative maximum or minimum?

Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .

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