(a) Explanation Given Information: The curve has the equation y = 1 2 π e − z 2 2 . Formula used: If f ( x ) = c ⋅ u ( x ) , where, c is a constant and u ( x ) is a differentiable function of x , then, f ′ ( x ) = c ⋅ u ′ ( x ) According to the property of derivatives, if y = e x , where, u is a differentiable function of x , d y d x = e x According to the power rule of differentiation, d y d x = n x n − 1 Calculation: Consider the provided equation, y = 1 2 π e − z 2 2 To find the highest point, differentiate both sides with respect to z , d y d z = d d z ( 1 2 π e − z 2 2 ) = 1 2 π d d z ( e − z 2 2 ) Apply the properties of derivative and simplify, d y d z = 1 2 π ( e</ (b) To determine To graph: The function, y = 1 2 π e − z 2 2 , using a graphing utility.

11th Edition

ISBN: 8220100546235

Author: Reynolds

Publisher: CENGAGE L

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Chapter 11.2, Problem 37E

(a)

To determine

To calculate: The value of z at which the curve y=12πe−z22 will be at the highest point.

(b)

To determine

To graph: The function, y=12πe−z22, using a graphing utility.

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Chapter 11.2, Problem 36E

Chapter 11.2, Problem 38E

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The value of z at which the curve y = 1 2 π e − z 2 2 will be at the highest point.

Solution Summary: The author explains how to calculate the value of z at which the curve y=1sqrt2pi