To determine To calculate: The interval on which the function f ( x ) = x 2 + 4 x is increasing or decreasing. Explanation Given: The function is: f ( x ) = x 2 + 4 x Formula used: The derivative property as; d d x ( u v ) = u v ′ − v u ′ v 2 Calculation: Consider the provided function, f ( x ) = x 2 + 4 x In order to find the intervals, calculate f ' ( x ) . Then, f ' ( x ) = d d x ( x 2 + 4 x ) = x d d x ( x 2 + 4 ) − ( x 2 + 4 ) d d x x x 2 = x ( 2 x ) − ( x 2 + 4 ) x 2 = x 2 − 4 x 2 Now, equate f ' ( x ) to 0. x 2 − 4 x 2 = 0 x 2 − 4 = 0 ( x − 2 ) ⋅ ( x + 2 ) = 0 x = − 2 , 2 And f ' ( x ) does not exist if; x 2 = 0 x = 0 The values of x divide the x -axis into 4 intervals ( − ∞ , − 2 ) , ( − 2 , 0 ) , ( 0 , 2 ) , ( 2 , ∞ )

12th Edition

ISBN: 9780135335215

Author: Lial

Publisher: PEARSON

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Chapter 12.1, Problem 16E

To determine

To calculate: The interval on which the function f(x)=x2+4x is increasing or decreasing.

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Chapter 12.1, Problem 15E

Chapter 12.1, Problem 17E

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