NOTES m 51 The Natural Legarithmie Fm: Entegratib m Day 1 aim/1?
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Amiications of Derivatives
Tangent Line Equations:
1. What is the slope of the tangent line?
a. Find the derivative of the function - formula for the slope of any tangent line to the f
5.1 & 5.2 Scavenger Hunt
Complete all work on lined paper.
1. Find the derivative of
= ln 2 + 3
2. Find the derivative of
3. Find the derivative of
= ln sin3
4. Find the derivative of
5 + 8 ln = 7
5. Find the derivative of
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Rectiiinear Motion Name?
I 1 Date ilr:
1. The table represents data collected in an experiment on a new type of electric engine for a small
neighborhood vehicle (i.e., one that is licensed for travel on roads with s
367 thimtzation Name:
Day 3 Date: Hr:
1. Find the dimensions of the rectangle of largest area that has its base on the xaxis and its other two
vertices above the x-axis and lying on the parabola y = 9 ~ x2.
2. Find the max area of a rectangle with upper
3.? Optimization Name:
Day 2 Date: Hr:
1. Find two positive numbers such that their product is 192 and the sum of the first number and three
times the second number is a minimum.
8 and 2H
2. A tank with a rectangular base and rectangular sides is open at
NOTES ._. 3."? thimization . may 1 . 2/2il?
Optimization finding the (absolute) maximum or minimum value in a situation that is
modeled by a function, within given constraints.
Game Plan for solving Optimization problems:
1. Write an equation for the valu
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NOTES ~ 33 Optimization m I 2 ._, 2/311?
1 What needs to be optimized? (write on equation)
2 is the equation a function of only one variable? (relating equation a substitution)
3. What are the endpoints and critical numbers? (derivative=0& dete
2. y = 5x4 +tanx
AP Calculus AB m Exam Review Day 3 m Weview Quiz
6x2/3 5951/2 =- 7
22 Basic Differentiatien Ruies
2 cos 2x
8. xysin(x+y) = 3
2.3 Product & Quotient ules
2.5 Impjcit Differentiat
AP Calculus Exam Review #4 Name:
(25) Date: Hr:
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AP Calculus AB Exam Review N Day 2 Preview Quiz
1.4 Continuity & OnewSided Limits
1. Find the xvalues (if any) where f is not continuous. State whether each discontinuity is
removable or nonremovablen
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QUlDELlNES FOR RELATED RATE PROBLEMS
1. Determine the rate that is given and the rate that is required to find,
2. Write a relating equation involving only those two quantities (some substitution
mag be required to eliminate other unwanted variables).
3.? @btimization Name:
Day 1 Iate: Hr:
1. Determine the maximum product of two positive numbers whose sum is 8.
2. The SJm of two numbers at and y is 10. Each number must be at least 2. Find themaximum and
minimum values of the product of th
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2.1 The Derivative and the Tangent Line Problem (Day 2) - 10/13/16
The limit used to define the slope of the tangent line (see yesterdays notes) is also used to
define one of two fundamental operations in Calculus -'cziifferentiation.l
tliie Process 3;?
2.1 The Derivative and the Tangent Line Probiem (Day 13 - 10/12/16
What does it mean to say that a fine is tangent to a curve at a point?
We can approximate the siope of the tangent line sing amthrough the point (P) of tangency and
a second point on the