Explanation Formula used : (1) The formula of differentiation of exponential function is, d d x e x = e x (2) The formula of differentiation of power component function is, d d x ( x n ) = n x n − 1 (3) The formula of the product chain rule of differentiation is, d d x ( u v ) = u d d x ( v ) + v d d x ( u ) Given information: The given function is, f ( x ) = x e − x 2 (1) Calculation: Differentiate the equation (1) both side with respect to x for the value of the first derivative of the function f ( x ) , f ′ ( x ) = d d x ( x e − x 2 ) [ Chain rule ] = x d d x ( e − x 2 ) + e − x 2 d d x ( x ) = x e − x 2 d d x ( − x 2 ) + e − x 2 = x e − x 2 ( − 2 x ) + e − x 2 Simplify the above expression, f ′ ( x ) = x e − x 2 ( − 2 x ) + e − x 2 = ( 1 − 2 x 2 ) e − x 2 For the critical number of the function, f ′ ( x ) = 0 <

Applied Calculus for the Managerial, Life, and Social Sciences

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ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Chapter 5.4, Problem 46E

To determine

The absolute extrema of the function.

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Chapter 5.4, Problem 45E

Chapter 5.4, Problem 47E

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Applied Calculus for the Managerial, Life, and Social Sciences

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Prob. 24E Ch. 5.5 - Prob. 25E Ch. 5.5 - Prob. 26E Ch. 5.5 - Prob. 27E Ch. 5.5 - find the derivative of the function. 28...Ch. 5.5 - Prob. 29E Ch. 5.5 - Prob. 30E Ch. 5.5 - Prob. 31E Ch. 5.5 - Prob. 32E Ch. 5.5 - Prob. 33E Ch. 5.5 - Prob. 34E Ch. 5.5 - Prob. 35E Ch. 5.5 - Prob. 36E Ch. 5.5 - Prob. 37E Ch. 5.5 - Prob. 38E Ch. 5.5 - Prob. 39E Ch. 5.5 - Prob. 40E Ch. 5.5 - Prob. 41E Ch. 5.5 - Prob. 42E Ch. 5.5 - Prob. 43E Ch. 5.5 - Prob. 44E Ch. 5.5 - Prob. 45E Ch. 5.5 - Prob. 46E Ch. 5.5 - Prob. 47E Ch. 5.5 - Prob. 48E Ch. 5.5 - Prob. 49E Ch. 5.5 - Prob. 50E Ch. 5.5 - Prob. 51E Ch. 5.5 - Prob. 52E Ch. 5.5 - Prob. 53E Ch. 5.5 - Prob. 54E Ch. 5.5 - Prob. 55E Ch. 5.5 - Prob. 56E Ch. 5.5 - Prob. 57E Ch. 5.5 - Prob. 58E Ch. 5.5 - Prob. 59E Ch. 5.5 - Prob. 60E Ch. 5.5 - Prob. 61E Ch. 5.5 - Prob. 62E Ch. 5.5 - Prob. 63E Ch. 5.5 - Prob. 64E Ch. 5.5 - Prob. 65E Ch. 5.5 - Prob. 66E Ch. 5.5 - Prob. 67E Ch. 5.5 - Prob. 68E Ch. 5.5 - Prob. 69E Ch. 5.5 - Prob. 70E Ch. 5.5 - Prob. 71E Ch. 5.5 - Prob. 72E Ch. 5.5 - 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The absolute extrema of the function.

Solution Summary: The author explains the formula of differentiation of exponential function and power component function.

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