BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 5.4, Problem 32E

a

To determine

To show: that the critical numbers of C occur at the numbers

Expert Solution

Answer to Problem 32E

critical number of c occur at the number t where C(t)=(f(t)+g(t))

Explanation of Solution

Given information: C(t)=1t0r[f(s)+g(s)]ds

C(t)=1t0r[f(s)+g(s)]ds

  C(t)=1t{f(t)-f(0)+g(t)-g(0)}

  C(t)=1t{f(t)-f(0)+g(t)-g(0)}

  C(t)=1t{f(t)+g(t)}

Hence , critical number of c occur at the number t where C(t)=(f(t)+g(t))

b

To determine

the length of time T for the total depreciation .

Expert Solution

Answer to Problem 32E

  f(t)=29v15

Explanation of Solution

Given information:

   f(t)=v15v450t    if    0<t30          0                 if     t>0and g(t)=vt212900           t>0

  f(t)=030v15 dt- 030v30dtf(t)=v15·30v450·30f(t)=2v-v15f(t)=29v15

c

To determine

the length of absolute minimum .

Expert Solution

Answer to Problem 32E

we get minimum value 0 .

Explanation of Solution

Given information: C on (0,T]

The absolute minimum value for maxima and minima . differentiating above equation equate to zero we get minimum value 0

d

To determine

To sketch: the graph of C.

Expert Solution

Answer to Problem 32E

the graph of C and f+g is as liner.

Explanation of Solution

Given information: f+gin the same coordinate.

the graph of C and f+g is as liner.

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