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| f(x) is increasing when.... |
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Definition
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| f(x) is decreasing when... |
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| f(x) is concave up when... |
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| f(x) is concave down when... |
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| f(x) has a point of inflection where... |
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| To find the absolute extreme values of f(x) on [a,b]... |
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Definition
| Use the Candidate Test. Find the y-coordinates (using the equation of f) at critical points and end points. |
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| To find the relative extreme values of f(x) on (a,b)... |
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Definition
| Conduct a sign study on f'(x) or use the Second Derivative Test |
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| To find where f(x) has points of inflection... |
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Definition
| Conduct a sign study on f''(x) |
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| According to the 2nd Derivative Test, a function f(x) has a relative maximum at x=c if.... |
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| According to the 2nd Derivative Test, a function f(x) has a relative minimum at x=c if.... |
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| If f'(x) changes from positive to negative at x=c, then... |
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Definition
| f(x) has a relative maximum at x=c. |
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| If f'(x) changes from negative to positive at x=c, then... |
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Definition
| f(x) has a relative minimum at x=c |
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| If f''(x) changes from positive to negative at x=c, then... |
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Definition
| f(x) has a point of inflection at x=c and f'(x) has a relative maximum at x=c. |
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| If f''(x) changes from negative to positive at x=c, then... |
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Definition
| f(x) has a point of inflection at x=c and f'(x) has a relative minimum at x=c. |
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| A function f(x) has an absolute maximum on an open interval (a,b) at x=c if... |
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Definition
| the only critical point of f(x) on (a,b) occcurs at x=c and f'(x) changes from positive to negative at x=c. |
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| A function f(x)has an absolute minimum on an open interval (a,b) at x=c if... |
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Definition
| the only critical point of f(x) on (a,b) occurs at x=c and f'(x) changes from negative to positive at x=c. |
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| Mean Value Theorem for Derivatives states that... |
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Definition
| If f(x) is continuous on [a,b] and differentiable on (a,b), then there is at least one value of c in (a,b) such that[image] |
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