April 16
section covered in text:
3.6. Implicit Differentiation
objective:
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to be able to find the derivative of a function implicitly
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to be able to use implicit differentiation to find
the equation to a tangent line to a function at a given point
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to be able to find horizontal and vertical tangents
to the curves of implicitly stated functions
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to be able to find derivatives of inverse trigonometric
functions
key ideas and/or vocabulary
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implicit differentiation
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derivatives of inverse trigonometric functions
solved problems - using key ideas
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differentiating an explicit and implicit function,
#1
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using implicit differentiation, #7
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finding the equation to the tangent line of a curve,
#15
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finding horizontal and vertical tangents to the curves
of implicitly stated functions, 18,21
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derivative of inverse trigonomeric function, #25
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orthogonal curves, #33,38
group work
none
announcements
Homework. #2,6,12,16,26,34
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QUESTION OF THE DAY
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Let g(x) = x1/2. Find
the slope of the tangent line to the graph of g at the point (4,2).
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SOLUTION
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SOLUTION.
f'(x) = 0.5x-1/2.
At the point x = 4 the slope of the tangent
line is 0.5(1/2).
The equation of the tangent line to the point
(4,2) is
y - 2 = .5(x - 4).
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