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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.