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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

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Section
BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

The equation for the standard normal probability distribution is

y = 1 2 π e z 2 / 2

(a) At what value of z will the curve be at its highest point?

(b) Graph this function with a graphing utility to verify your answer.

(a)

To determine

To calculate: The value of z at which the curve y=12πez22 will be at the highest point.

Explanation

Given Information:

The curve has the equation y=12πez22.

Formula used:

If f(x)=cu(x), where, c is a constant and u(x) is a differentiable function of x, then,

f(x)=cu(x)

According to the property of derivatives, if y=ex, where, u is a differentiable function of x,

dydx=ex

According to the power rule of differentiation,

dydx=nxn1

Calculation:

Consider the provided equation,

y=12πez22

To find the highest point, differentiate both sides with respect to z,

dydz=ddz(12πez22)=12πddz(ez22)

Apply the properties of derivative and simplify,

dydz=12π(e</

(b)

To determine

To graph: The function, y=12πez22, using a graphing utility.

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Chapter 11 Solutions

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