Il in the blanks. et f be a differentiable function. the first derivative of f changes sign from plus to minus at x = a, then f has local at z = a. the first derivative of f changes sign from minus to plus at x = a, then f has local at z = a. the first derivative of f is positive for all real numbers, then the function f is the first derivative of f is negative for all real numbers, then the function f is the second derivative of f is positive for all real numbers, then the graph of f is concave the second derivative of f is negative for all real numbers, then the graph of f is concave

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.1: Inverse Functions
Problem 18E
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Fill in the blanks.
Let f be a differentiable function.
If the first derivative of f changes sign from plus to minus at x = a, then f has local
at z = a.
If the first derivative of f changes sign from minus to plus at x = a, then f has local
at x = a.
If the first derivative of f is positive for all real numbers, then the function f is
If the first derivative of f is negative for all real numbers, then the function f is
If the second derivative of f is positive for all real numbers, then the graph of f is concave
If the second derivative of f is negative for all real numbers, then the graph of f is concave
Transcribed Image Text:Fill in the blanks. Let f be a differentiable function. If the first derivative of f changes sign from plus to minus at x = a, then f has local at z = a. If the first derivative of f changes sign from minus to plus at x = a, then f has local at x = a. If the first derivative of f is positive for all real numbers, then the function f is If the first derivative of f is negative for all real numbers, then the function f is If the second derivative of f is positive for all real numbers, then the graph of f is concave If the second derivative of f is negative for all real numbers, then the graph of f is concave
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