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# P11 - Project 11 MAC 2311 1 Examine the function f(x = x3...

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Project 11 MAC 2311 1. Examine the function f ( x ) = x 3 - 3 x . From precalculus, what should be the two distinct possibilities for the number of turning points of any cubic (degree 3) polynomial function? In order for a smooth graph to “turn around”, what value would the slope of the curve need to be at the turning point? (Illustrate with a picture.) Is the reverse true (can a graph have that slope without turning around)? Find the values of x at which f ( x ) has horizontal tangent lines. Find the zeros ( x -intercepts) of f ( x ) . Calculate the slope of f ( x ) at EACH of its zeros. How many horizontal tangent lines does the function g ( x ) = x 3 + 3 x have? Can it turn around? How many zeros does it have? Sketch the functions f ( x ) and g ( x ) , incorporating the above information and labelling the points where the horizontal tangent lines occur. Based on your discoveries so far, how does the derivative of a cubic function determine the number of turning points that it has?

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2. A population of wolves increases so that the number of wolves
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P11 - Project 11 MAC 2311 1 Examine the function f(x = x3...

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