warm up problems 1.if, find f (x). 2.if, find f (x). 3.given the graph of f (x), find all intervals...
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Warm up Problems1.If , find f (x).
2.If , find f (x).
3.Given the graph of f (x), find all intervals where f (x) is increasing.
12 3f x x
23 2f x x
2
-2
5 10
f '(x)
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Interpreting the Derivative
New Notation: If y = f (x), then
derivative of
with respect
to
dyf x y
dxx
x a
dyf a
dx
3 23d
x xdx
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Ex. The cost C, in dollars, of building a new stage at McKinley High that has area A square feet is given by C = f (A). What are the units of f (A)?
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Ex. The cost, in dollars, for the seven dwarves to extract T tons of ore from their mine is given by M = f (T). What does f (2000) = 100 mean?
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Ex. Suppose P = f (t) is the population of Springfield, in millions, t years since 1990. Explain f (15) = -2.