Clicker Question 1
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What is the instantaneous rate of
change of f (x ) = ln(x ) at the point
x = 1/10?
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A. 1/10
B. 10
C. 0
D. ln(1/10)
E. undefined
Clicker Question 2
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What is the slope of the tangent line to
the curve y = x 3/2 at the point x = 9 ?
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A. 9/2
B. 27
C. 3
D. 9/4
E. 3/2
Clicker Question 3
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What is an equation of the secant line
connecting (2, f (2)) and (3, f (3)) for the
function f (x ) = x 3 ?
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A. y = 19x 3
B. y = 19x – 30
C. y = -19x + 46
D. y = (1/19)x – 7
E. y = 19x + 30
Clicker Question 4
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What is an equation of the tangent line
at the point (2, f (2)) for the function
f (x ) = x 3 ?
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A. y = 8x – 8
B. y = 12x 3 – 16
C. y = 12x – 16
D. y = 12x – 20
E. y = 8x – 16
What do we know? (11/9/11)
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What limits are, how to see them on a
graph, and how to (try to) compute
them algebraically.
Distinguish between limits which are
two-sided, one-sided, infinite, at
infinity, and non-existent.
What else?
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To distinguish between the average rate of
change of a function between two points (precalculus) and the instantaneous rate of change
at one point (calculus!).
Know the definition and idea of the derivative
of a function.
Use the definition to compute derivatives
algebraically given the function’s formula, or
graph them given the function’s graph.
And what else?
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Know the derivative functions of the
most basic elementary functions:
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All power functions (using the Power Rule)
The sin, cos and tan trig functions
The natural exponential and log functions
(i.e., ex and ln(x ))
Some things
we don’t yet know
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How to compute the derivatives of
combinations of functions (i.e., sums,
differences, products, quotients,
compositions, and inverses.
How to apply the derivative to various
kinds of “real-life” problems.
How to reverse the derivative process
(“anti-derivatives”).
Assignment
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Friday’s class is optional
(no attendance, no clickers).
Optional worksheet on derivatives is
handed out.
Test #2 is Monday (11/14).