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Analyzing Functions
Chapter 4, Kennedy, Waits, Demaney
17
Mathematics
12th Grade
10/23/2021

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Term
f(x) is increasing when....
Definition
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f(x) is decreasing when...
Definition
[image]
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f(x) is concave up when...
Definition
[image]
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f(x) is concave down when...
Definition
[image]
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f(x) has a point of inflection where...
Definition
f''(x) changes signs.
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To find the absolute extreme values of f(x) on [a,b]...
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)...
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...
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....
Definition
[image]
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According to the 2nd Derivative Test, a function f(x) has a relative minimum at x=c if....
Definition
[image]
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If f'(x) changes from positive to negative at x=c, then...
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...
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...
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...
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...
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...
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...
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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