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What would the graph of the derivative look like? Calculus

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What would the graph of the derivative look like? Calculus for Everyone Ex 1 Find the slope of the graph (using the derivative rules) ... – PowerPoint PPT presentation

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Title: What would the graph of the derivative look like? Calculus


1
Calculus for Everyone
In the middle of difficulty lies
opportunity Albert Einstein

2.1 Review
2
Calculus for Everyone
Review for 2.1 The Definition of the
Derivative p.153 1,3,4,5-9,11,13,15,16
3
Calculus for Everyone
Please be sure and label your Review paper 2.1
Review and do NOT put more than one review per
paper!
4
Calculus for Everyone
Calculus Concepts you must know
5
Calculus for Everyone
What does it mean for a line to be tangent to a
curve at a point?
6
Calculus for Everyone
Consider the curve At what point is
the derivative going to be positive? negative? p
ositive? constant?
7
Calculus for Everyone
Consider the graph of a parabola. What would the
graph of the derivative look like?
8
Calculus for Everyone
Ex 1 Find the slope of the graph (using the
derivative rules)
9
Calculus for Everyone
Ex 2 Find the slopes of the tangent lines to the
graph of (using the limit def)
10
Calculus for Everyone
When does the tangent line to a curve not
exist? At a vertical tangent line to a point on
a curve (vertical lines have no slope and that
is what the limit gives you)
11
Calculus for Everyone
At what other places does the derivative not
exist?
12
Calculus for Everyone
The Derivative of a Function and the process
to get there is calleddifferentiation
13
Calculus for Everyone
The Derivative of a Function is the slope of
the tangent line at that point. derivative
slope
14
Calculus for Everyone
Note the Definition of the Derivative of a
Function p.97
15
Calculus for Everyone
And the other symbols for differentiation p.97
16
Calculus for Everyone
Example 4 Finding the Derivative by the Limit
Process
17
Calculus for Everyone
Example 5 Finding the Derivative WRT to t
18
Calculus for Everyone
HW example 34
19
Calculus for Everyone
Example 5A Finding the Equation Line at (1,2)
20
Calculus for Everyone
How do you find the derivative using your
calculator? nderiv
21
Calculus for Everyone
Test on 2.1 Friday
22
Calculus for Everyone
Any other questions about 2.1.3???
23
Calculus for Everyone
24

You Can Do This !
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