Graph the polynomial P(x)=x5+x4−7x3−x2+6x+3 by using a graphing device. Find the x and y intercepts and the coordinates of all local extrema. Describe the end behavior of the polynomial.
Based from the graph, the x intercepts can be approximated as −3.05,1.35 and 1.80. On the other hand, the value of the y intercept is 3. Also, the coordinates of the local maxima are (−2.45,33) and (0.5,5). While the coordinates of the local minima are (−0.60,0.80) and (1.60,−1.75). More over, the function has an end behavior of y→∞ as x→∞ and y→−∞ as x→−∞.
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