   Chapter 11.2, Problem 42E ### Mathematical Applications for the ...

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

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

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

# In Problems 39-42, find any relative maxima and minima. Use a graphing utility to check your results. y = x 2 e x

To determine

To calculate: The relative maxima or minima for the function, y=x2ex.

Explanation

Given Information:

The function is y=x2ex.

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

According to the quotient rule of derivatives,

ddx(fg)=gffgg2

Calculation:

Consider the provided function,

y=x2ex

To find the relative minimum, differentiate both sides with respect to x,

dydx=ddx(x2ex)=ddx(x2ex)

Apply the quotient rule for derivatives,

dydx=(ex)(ddx(x2))x2(ddx(ex))(ex)2

Simplify the derivative using the quotient rule of derivatives,

dydx=(ex)(2x21)x2(ex)e2x=2xexx2exe2x

Take ex common from the numerator,

dydx=xex(2x)e2x=2xx2ex

To calculate the value of mean, the value of dydx should be equal to zero

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