# Shared Flashcard Set

## Details

Derf Calculus Ch 2
continuity and derivatives
15
Mathematics
09/14/2012

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