# that the critical numbers of C occur at the numbers ### Single Variable Calculus: Concepts...

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

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

Expert Solution

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

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

Expert Solution