Explanation Formula used : The formula of differentiation of exponential function is, d d x e x = e x The formula of differentiation of power component function is, d d x ( x n ) = n x n − 1 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 equation of the graph is, f ( x ) = 2 e − x 2 (1) Calculation: Differentiate the equation (1) both side with respect to x , f ′ ( x ) = d d x ( 2 e − x 2 ) [ Chain rule ] = 2 d d x e − x 2 = 2 e − x 2 d d x ( − x 2 ) = − 4 x e − x 2 Differentiate the above equation both side with respect to x for the second derivative of the function f ( x ) , f ″ ( x ) = d d x ( − 4 x e − x 2 ) = − 4 x d d x e − x 2 + ( − 4 e − x 2 ) d d x x = − 4 x ( − 2 x e − x 2 ) + ( − 4 e − x 2 ) = 4 e − x 2 <

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 5.4, Problem 40E

To determine

The inflection point of the function f(x)=2e−x2 .

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Chapter 5.4, Problem 39E

Chapter 5.4, Problem 41E

Chapter 5 Solutions

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 inflection point of the function f ( x ) = 2 e − x 2 .

Solution Summary: The author explains the inflection points of the function f(x)=2e-x

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The inflection point of the function f(x)=2e−x2 .

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Chapter 5 Solutions