Unformatted text preview: D is a point c in D such that
f (x ) ≤ f (c ) for all x ∈ D . 2 A global minimum for f on D is a point c in D such that
f (x ) ≥ f (c ) for all x ∈ D . 3 If there is an interval i in D containing c such that f (c ) is a
maximum on I , then we call f (c ) a local maximum of f . 4 If there is an interval I in D containing c such that f (c ) is a
minimum on I , then we call f (c ) a local minimum of f . Outline Symmetry Positive/Negative Increasing/Decreasing Maximum/Minimum The Diﬀerence Quotient Example
Discuss the local and global maximums and Minimums of the
function graphed below. Outline Symmetry Positive/Negative Increasing/Decreasing Maximum/Minimum The Diﬀerence Quotient The Diﬀerence Quotient
Deﬁnition
Suppose f is a function from D into R. The diﬀerence quotient of
f over an interval [a, b ] in in D is:
∆y
f (b ) − f (a)
f (x + h) − f (x )
=
=
∆x
b−a
h
where h = b − a and a = x .
Example
Compute and simplify the diﬀerence quotient of:
1 2 f (x ) = x 2 − 3.
4
f (x ) = .
x...
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 Spring '14
 K.JPlatt
 Math, Calculus, Algebra, Difference Quotient, Department of Mathematics, Snow College

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