m408k_test3_review - Test 3 review Drawing the graph of a...

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Test 3 - review Drawing the graph of a function. Determine the intervals where f increases ( f > 0), decreases ( f < 0), is concave up ( f > 0), is concave down ( f < 0). Horizontal asymptotes: find lim x →∞ f ( x ) and lim x →-∞ f ( x ). Vertical asymptotes: find points c where lim x c - f ( x ) = ±∞ or lim x c + f ( x ) = ±∞ . Optimization problems. 1) Express the quantity that you want to optimize Q as a function of only one variable x (usually you start with a function of more variables, but there is a constraint that they satisfy such that you can express all the variables in terms of one of them). 2) Differentiate Q ( x ) and solve the equation Q ( x ) = 0 for x . The absolute maximum or minimum of Q appears either there or at an end point of the domain. Antiderivatives. F ( x ) is an antiderivative of f ( x ) ⇐⇒ F ( x ) = f ( x ) . Examples: sketch the graph of antiderivatives, find a particular antiderivative of a function (determine the constant such that some condition is satisfied).
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