Chapter 3: Derivatives
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Transcript of Chapter 3: Derivatives
![Page 1: Chapter 3: Derivatives](https://reader034.fdocuments.us/reader034/viewer/2022050803/5681301e550346895d959d3c/html5/thumbnails/1.jpg)
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Chapter 3:
Derivatives
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d xdx
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( )s t
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ln e
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If a particle is moving right (forward),
then v(t) …
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2(sin )d xdx
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If f(x) is differentiable for all values of x, then the graph of f(x) is...
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A particle is changing directions when…
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(cos )d xdx
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If a particle is speeding up, then …
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loga b
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A particle is standing still when …
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(tan )d xdx
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(cot )d xdx
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If the graph of f(x) is DECREASING, then the graph of f’(x) is __________.
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(sec )d xdx
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( )v t
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If f(x) is continuous but the derivative of f(x) is undefined then the following things could exist…
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( )xd edx
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If the graph of the derivative is negative, then the graph of the
function is ________.
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(ln )d udx
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( )ud adx
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When is net change in position (displacement) and total distance traveled the same?
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sin xd edx
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If a particle is moving left, then v(t)…
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If the graph of the derivative is positive, then the graph of the function is
________.
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Given function u(x) and v(x),
d uvdx
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If a particle is slowing down, then …
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(sin )d xdx
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If the graph of a function is increasing, then the graph of the derivative is
______.
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24 3d xdx
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If the graph of a function is decreasing, then the graph of the derivative is
______.
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21d
dx x
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How do you find the average acceleration on [a,b] given the
velocity function v(t)?
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(csc )d xdx
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How do you find the average velocity on [a,b] given the
position function, s(t)?
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cos 4d xdx
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d f g xdx
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If the graph of f(x) has an extrema at x= b, then the graph of f’(x) has a
_________ at x = b.
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2log 5d xdx
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cot5 xddx
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ln sind xdx
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Given function u(x) and v(x),
d udx v
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2xd edx
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cotd xdx
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In what case would the graph of f ’(x) have a zero at x = b, and the graph of f(x) not have an extrema at x = b.