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Mock Gateway 3

# Mock Gateway 3 - formulas are required just label the...

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Mock Gateway III (Graphs) 1. (20 pts) Find the absolute minimum and maximum of f ( x ) = 15 x 4 - 15 x 2 + 31 on the interval [ - 1 , 2]. 2. (10 pts) Find the points where f has a local maximum or minimum on the given domain and identify each point as a local maximum or local minimum. If there is no local maximum or minimum, explain (briefly) why.. f ( x ) = x 2 + 3 x , 0 < x <

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3. (28 pts) For the given derivative of a function f , f ( x ) = ( x - 1)( x + 1), (a) What are the critical numbers of f ? (b) On what intervals is f increasing? (c) On what intervals is f decreasing? (d) At what points, if any, does f assume a local maximum or local minimum value? 4. (10 pts) Sketch the graph of a function that satisfies the given conditions. No

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Unformatted text preview: formulas are required - just label the coordinate axes and sketch an appropriate graph. f (-2) =-1 , f (0) = 0 , f (2) = 1 , lim x →-∞ f ( x ) = 0 , lim x →∞ f ( x ) = 0 5. (12 pts) The graph of the ﬁrst and second derivative of a function y = f ( x ) are shown. Add to the picture a sketch of the approximate graph of f , given that the graph passes through the point P . 6. (20 pts) The accompanying ﬁgure shows a portion of the graph of a twice-diﬀerentiable function y = f ( x ). At each of the ﬁve labeled points, classify y and y 00 as positive, negative or zero....
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