How do we know that we have found a local maximum? The demand x for a good is related to its price p via the function:p=32e-0-0.2x At the stationary point,At the stationary point,At the stationary point,At the stationary point,None of the aboved² TRdx²d²TRdx²d² TRdx²d² TRdx²= .6e¹ <0 therefore local max-1=-.5e=-.2e=-1<0 therefore local max<0 therefore local max-.3e-1 <0 therefore local max

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The demand x for a good is related to its price p via the function: p=3e-0.2x

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.4: Average Rate Of Change Of A Function

Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

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Question

How do we know that we have found a local maximum?

The demand x for a good is related to its price p via the function:
p=32e-0
-0.2x

At the stationary point,
At the stationary point,
At the stationary point,
At the stationary point,
None of the above
d² TR
dx²
d²TR
dx²
d² TR
dx²
d² TR
dx²
= .6e¹ <0 therefore local max
-1
=-.5e
=-.2e
=
-1
<0 therefore local max
<0 therefore local max
-.3e-1 <0 therefore local max

Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .

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