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Practice Test 1 Answer Key - Calculus II | MTH 252, Exams of Calculus

Portland Community College Calculus

Material Type: Exam; Class: Calculus II; Subject: Math; University: Portland Community College; Term: Spring 2007;

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

koofers-user-ce2 🇺🇸

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MTH 252 – Practice Test 1

Part A: No Calculator allowed for these questions

1. Find the critical numbers for the function

() ( )( )

35ht t t=+ −

. Then state all local minimum

and maximum points on h after first performing a first derivative test. Show all relevant work

in a well-organized manner; you need not write any further explanation.

2/2/2007 0:36AM

1 / 10

Partial preview of the text

Download Practice Test 1 Answer Key - Calculus II | MTH 252 and more Exams Calculus in PDF only on Docsity!

MTH 252 – Practice Test 1

Part A: No Calculator allowed for these questions

1. Find the critical numbers for the function ( ) ( )( )

5 h t = t + 3 t − 5. Then state all local minimum

and maximum points on h after first performing a first derivative test. Show all relevant work

in a well-organized manner; you need not write any further explanation.

MTH 252 Practice Test 2

2. Find the absolute minimum value of the function ( )

3 2 f x = x − 6 x + 9 x + 4 over the interval

[ 0, 2^ ].^ Show all of the documentation discussed and illustrated in class.

Evaluate each of the following limits using L’Hopital’s Rule where appropriate. Make sure that

you present your work in a manner consistent with that exemplified in lecture.

a. Evaluate

lim 3 sin

1/26/2007 4:52PM

2 / 9

MTH 252 Practice Test 2

d. Evaluate

0 2

lim x → 1 cos x 1 cos x

⎢ −^ − ⎥

10/15/2006 3:35PM

4 / 9

MTH 252 Practice Test 2

4. A certain function, y = f ( x ), is continuous and differentiable

at every point along the interval [ 0,4]. Along this interval

f ( x )has exactly two critical numbers: 1 and 3. Thesecond

derivative of f ( x )is shown in Figure 1. The question is this:

which is greater, f ( ) 1 or f ( 3 )? Write enough of an

explanation so that your reasoning is readily apparent.

A sketch might help your explanation.

5. The function ( )

sin( )

t g t t

does not have an absolute maximum value over the interval

. Briefly explain why this does not contradict the absolute maximum/minimum

theorem.

Figure 1: y = f ′′( x )

State in the provided spaces in Table 1, the form of the given limit and whether or not the

limit is of indeterminate form.

Table 1: Limits and student answers for problem 3

Limit Form of limit Is limit of indeterminate form?

lim x → ln

lim ln →

ln( )

lim 1 →+

8. Find, and completely simplify , the formula for f ′( x ) where ( )

x f x x

showing all

relevant work. That’s it – there’s nothing else to be done on this problem.

MTH 252 Practice Test 2

Part B: Use your calculator for all its worth on these problems

1. Suppose that ( )

x f x x

a. What are the critical number(s) of f?

b. Why can you not use a seconds derivative test to determine all of the local minimum and

maximum points on f?

c. State the local extreme points on f after first performing a first derivative test.

Practice Test 1 Answer Key - Calculus II | MTH 252, Exams of Calculus

Related documents

Partial preview of the text

Download Practice Test 1 Answer Key - Calculus II | MTH 252 and more Exams Calculus in PDF only on Docsity!

1. Find the critical numbers for the function ( ) ( )( )

2. Find the absolute minimum value of the function ( )

[ 0, 2^ ].^ Show all of the documentation discussed and illustrated in class.

⎢ −^ − ⎥

4. A certain function, y = f ( x ), is continuous and differentiable

at every point along the interval [ 0,4]. Along this interval

f ( x )has exactly two critical numbers: 1 and 3. Thesecond

derivative of f ( x )is shown in Figure 1. The question is this:

which is greater, f ( ) 1 or f ( 3 )? Write enough of an

5. The function ( )

sin( )

Figure 1: y = f ′′( x )

8. Find, and completely simplify , the formula for f ′( x ) where ( )

1. Suppose that ( )