Answered: Which of the following can the first…

Which of the following can the first derivative not be used to determine? 1. where the function is increasing or decreasing 2. Concavity 3. Critical Numbers 4. local maxima or local minima

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

Section4.1: Techniques For Finding Derivatives

Problem 4E: Find the derivative of each function defined as follows. y=5x4+9x3+12x2-7x

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Question

Which of the following can the first derivative not be used to determine?

1. where the function is increasing or decreasing

2. Concavity

3. Critical Numbers

4. local maxima or local minima

Formula Formula A function f ( x ) is also said to have attained a local minimum 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 a case f ( a ) is called the local minimum value of f ( x ) at x = a .

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