Unformatted text preview: al, then f (x) is constant
on the interval. f (b) - f (a)
is the average rate of
change of the function f between x = a and x = b. x:a x:a x:c Average rate of change: lim+ f (x) is the limit as x approaches a from the right (x 7 a). x:a TEST TO FIND INTERVALS WHERE f (x) IS
INCREASING/DECREASING 3. lim f (x) = f (c). Rate of Change and the Derivative lim f (x) is the limit as x approaches a from the left (x 6 a). Logarithmic Functions Domain: (0, q ) x:c x:a - Let y0 be the amount or number of some quantity initially
present (t = 0). Then the amount present at any time t is
y = y0ekt.
If k 7 0, this is exponential growth and k is called the growth
If k 6 0, this is exponential decay and k is called the decay
constant. 1. f (x) is continuous at x = c if
1. f (c) is defined. 2. lim f (x) exists. ONE SIDED LIMITS PROPERTIES OF LOGARITHMS FUNCTIONS 3. This means: 1. As x takes on values closer and closer (but not
equal) to a on both sides of a, the corresponding values of f (x) get closer and closer to L.
2. The value of f (x) can be made as close to L as
desired by taking values of x close enough to a. EXPONENTIAL GROWTH AND DECAY EQUATIONS OF LINES
with a > 0 lim f (x) = L is read as “the limit of f (x) as x approaches a is L.” x:a PROPERTIES OF EXPONENTIAL FUNCTIONS Relative (Local) Extrema CONTINUITY AT x = c Instantaneous rate of change
Slope of the tangent line
Critical numbers, intervals of increase and decrease of a
function, and relative extrema
Marginal revenue, marginal profit, and marginal cost
Velocity, v(t) 3 Find all critical numbers for f in (a, b).
Evaluate f (x) for all critical numbers in (a, b) (ignore any
critical numbers not within the given interval).
Evaluate f (x) at the given endpoints of the interval, namely
a and b.
The largest value for f (x) is the absolute maximum and the
smallest value for f (x) is the absolute minimum....
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- Spring '09
- Derivative, lim