Fundamentals of Calculus
Hill
Name:_
Graphing Functions & Their Derivatives to Determine Max/Min
A. Let
f(x) = 4 x 3 52 x 2 + 160 x for questions 1 6.
1.
Graph f(x) on the graphing calculator and make sure that the function fits in the view
window.
2.
Det
Fundamentals of Calculus
Name:_
Rational Functions Review 2
A. Identify the horizontal asymptotes, vertical asymptotes, x-intercepts and y-intercepts of each
function.
1. y =
2. y =
3. y =
4. y =
5.
6.
7.
y=
y=
B. Providetherequestedinformationandgrapheac
Fundamentals of Calculus
Areas/Volumes WS IV
Name:_
Determine the area between the given curves. Set up the integral and evaluate the integral using
the calculator.
1.
1. _
1._
2.
,
2. _
2._
Determine the volume of each area when rotated about the given a
Fundamentals of Calculus
Areas/Volumes WS III
Name:_
Determine the area between the given curves. Set up the integral and evaluate the integral using
the calculator.
1.
1. _
1._
2.
2. _
2._
3.
3. _
3._
4.
4. _
4._
Determine the volume of each area when ro
Fundamentals of Calculus
4-1 Initial Condition Problems
A differential equation is an equation that involves a derivative. Solve each differential equation for .
1)
2)
3)
4)
5) It is estimated that x months from now the population of a certain town will b
Fundamentals of Calculus
3-7(3) Optimization: Volume
Class Examples
1) A rectangular box with a square base and no top is to be constructed using a total of 120 square cm of
cardboard. Find the dimensions of the box of maximum volume.
2) An open box is to
Fundamentals of Calculus
3-7(2) Optimization: Border Problems
Class Examples
1) A printer needs to make a poster with a total area of 300 square inches. The poster will have 2 inch
margins on the sides and 1.5 inch margins on the top and bottom. What over
Fundamentals of Calculus
2-2(7) Examining Projectile Motion
When an object is subjected to gravity, its position function is given by
where t is measured in seconds, s (t) is measured in feet, is the initial velocity (velocity at t = 0), and is
the initia
Fundamentals of Calculus
2-2(5) Analyzing Horizontal Motion
Class Example: Do an analysis of the horizontal motion of a particle if its position is given by:
1) Find
2) Find where = 0.
0
3) Find
4) Find where = 0.
0
5) Describe the motion of the particle.
Fundamentals of Calculus
2-2(4) Analyzing Motion on a Horizontal Line
Objects can move along a line, either
or
.
When an object moves, its position changes over time.
Example 1) For , show its position on the number line for t = 0, 1, 2, 3, 4.
We can say
Fundamentals of Calculus
2-2 Analyzing Motion Quiz Review
1) The figure shows the acceleration and velocity
of an object as a function of time. Translate the
information given to a velocity and acceleration
sign chart.
2) For the times shown, tell whether