Term
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Definition
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Term
Four ways in which a
function can fail to be
differentiable at a point |
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Definition
• Discontinuity
• Corner/Point
• Cusp
• Vertical tangent |
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Term
| To justify a critical number: |
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Definition
| f'(x)=0 or does not exist |
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Term
| Justify f(x) is increasing. |
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Definition
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Term
Justify f(x) is decreasing.
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Definition
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Term
Justify f(x) is concave up.
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Definition
f"(x)>0 or
f'(x) is increasing.
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Term
Justify f(x) is concave down.
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Definition
f"(x)<0 or
f'(x) is decreasing. |
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Term
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Definition
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Term
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Definition
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Term
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Definition
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Term
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Definition
| f'(x)=0 or undefined and changes from positive to negative at x. |
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Term
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Definition
| f'(x)=0 or undefined and changes from negative to positive at x. |
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Term
| Intermediate Value Theorem: If f is continous on the interval [a,b], then... |
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Definition
| f must take on every value (height) from f(a) to f(b). |
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Term
| If f is differentable at a point, then... |
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Definition
| ...it must be continuous at that point. (Differentiability implies continuity.) |
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Term
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Definition
f"(x)=0 or undefined
AND changes sign |
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