Calculus Lab 4Difference Quotients and Derivatives
(edited from U. of Alberta)
Objective: To compute difference quotients and derivatives of expressions and
functions.
Recall Plotting Commands:
plot(cfw_expr1,expr2,x=a.b); Plots two Maple expressions on o
Partial HW Solutions to 4.3, 4.5, and 4.6
4.3 solutions:
#24 :
B (x) = 3x2/3 x
B (x) = 2x1/3 1 =
2 x1/3
x1/3
Critical numbers are x = 0, 8.
B (x) increasing on the interval (0, 8) and decreasing on (, 0) (8, ).
2
2
B (x) = x4/3 = 4
3
3
3( x)
B (x) always
Partial HW Solutions to 3.2 and 3.3
3.2 solutions:
#2 :
F (x) =
x 3x3/2
x
x 1 9 x1/2 (x 3x3/2 )(.5x1/2 )
x 4.5x .5 x + 1.5x
2
F (x) =
=
x
x
.5 x 3x
1
=
= 3
x
2x
1
Simplify rst: F (x) = x 3x. Thus, F (x) = 2x 3.
#3 : F (x) = x2 ex
Therefore F (x) = x2 (ex
Pre-Calculus Review Worksheet Answers
1. Write the equation of the line with slope 5 that passes through (3, 7).
y = 5(x + 3) + 7
2. Write the equation of the line with slope -4 and has a y -intercept of 9.
y = 4x + 9
3. Write the equation of the line tha
2.1 2.3 Selected Answers
2.1#8a.(i)6 (ii) 4.712 (iii) 6.13412 (iv ) 6.268371
b. 6.2 since the avg. velocities approach this number as the time interval gets shorter.
2.2#14
x2 2x
x2 2x2
at the given values are:
0, 1, 9, 19, 99, 999, 2, 3, 11, 101, 1001
Th
Lab 7-Families of Curves and First/Second Derivatives Again
Math isn't just about solving problems, it's also about finding/recognizing patterns. We will
explore a family of curves described in Problem 64 of Section 3.5:
Section 3.5 #64: Under certain cir
Lab 6-Trigonometric Functions, Chain Rule and Implicit Functions
d 2 f ( x)
is the second derivative of f(x). We will use this notation to help us
Recall
dx 2
answer the following questions involving trig functions.
Let us first define f(x) = cos x
> f:=x
Maple Lab 5
Produt Rule, Quotient Rule and Trigonometric Functions
Load the Calculus I Package by typing;
> with(Student[Calculus1]):
We already learned how Maple can find the derivative for you. Recall to take the
derivative of f(x)=3x10+7x2 , we define
Maple Lab 3
Objective: To become familiar with working with limits. To explore the connections
between limits, graphs and continuity. To explore asymptotic behavior.
1. Plotting Piecewise Defined Functions:
The following commands will allow you to plot a
MTH 251 Second Exam Review Sheet
Spring 2009
Exam 2 Procedures
You may use your graphing calculator for the exam.
You must show all of your work for full credit.
Academic integrity is expected.
I will supply reference page 5 for your test, but you wil