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Warm up Problems 1.If, find f (x). 2.If, find f (x). 3.Given the graph of f (x), find all intervals where f (x) is increasing.

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Interpreting the Derivative New Notation: If y = f (x), then

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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.

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4.1 Antiderivatives and Indefinite Integrals Defn. A function F(x) is an antiderivative of f(x) on an interval I if F '(x)=f(x) for all x in I. ex. Find.

4.1 Antiderivatives and Indefinite Integrals Defn. A function F(x) is an antiderivative of f(x) on an interval I if F '(x)=f(x) for all x in I. ex. Find.

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