4.1_First_Derivative_summer

# 4.1_First_Derivative_summer - 4.1 Applications of the First...

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4.1 Applications of the First Derivative Determining intervals where a function increases or decreases from a graph Identifying Critical Numbers of a function Determining intervals where a function increases or decreases from an algebraic definition When given a graph: Find the largest open intervals where f is increasing (intervals separated by semi-colons) Find the largest open intervals where f is decreasing (intervals separated by semi-colons) When no graph is given: The procedure to follow in determining the intervals where f increases or decreases is the following: Find all values of x for which f’(x)= 0 of f’(x) DNE. Identify the open intervals determined by these x values. Choose a test value, c, in each of these intervals. If f’(c) > 0, f is increasing in the interval. If f’(c) < 0, f in decreasing in the interval Let f(x) = x 2 + x – 20, Find the largest open intervals where f is increasing (intervals separated by semi-colons) Find the largest open intervals where f is decreasing (intervals separated by semi-colons) NOTE: If none, enter none

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4.1_First_Derivative_summer - 4.1 Applications of the First...

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