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Power Rule of Derivatives
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Sum/Difference Rule of Derivatives
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Product Rule of Derivatives
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Quotient Rule of Derivatives
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| Average Rate of Change of f(x) on [a,b] |
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| Limit Definition of Derivative |
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| Alternate Limit Definition of Derivative of f(x) at x=a |
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Definition
1. Derivative of f(x) at x=a.
2. Instantaneous Rate of Change of f(x) at x=a.
3. Slope of f(x) at x=a.
4. Slope of the line tangent to f(x) at x=a.
5. [image]
6. [image]
7. [image] |
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| The velocity of an object is... |
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Definition
| The rate of change of the object's position. |
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| The acceleration of an object is.... |
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Definition
| The rate of change of the object's velocity. |
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| Average Velocity on [a,b] |
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Definition
| [image] where s(t) is the object's position at time t. |
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| Average Acceleration on [a,b] |
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| [image] where v(t) is the object's velocity at time t. |
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| An object moves up/right/forward when... |
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Definition
[image],
where s(t) is the object's position at time t. |
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| An object slows down when... |
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Definition
| v(t) and a(t) have opposite signs |
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| An object speeds up when... |
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Definition
| v(t) and a(t) have the same signs |
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| An object moves down/left/backwards when... |
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Definition
[image],
where s(t) is the object's position at time t. |
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| An object is not moving when... |
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Definition
[image],
where s(t) is the object's position at time t. |
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| List the four ways in which a function could fail to be differentiable at x=a |
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Definition
f(x) is not differentiable at x=a if f(x) has a cusp, corner point or vertical tangent line at x=a.
4. Any discontinuity
at x=a. |
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