Solve the Problem $f ( x ) = 2 x ^ { 4 } - 7 x ^ { 3 } + 11 x - 4$

question 262

Essay

Solve the problem.
-For the polynomial function f(x) $f ( x ) = 2 x ^ { 4 } - 7 x ^ { 3 } + 11 x - 4$ a) Find the x- and y-intercepts of the graph of f. Round to two decimal places, if necessary.
b) Determine whether the graph crosses or touches the x-axis at each x-intercept.
c) End behavior: find the power function that the graph of f resembles for large values of |x $| x |$ d) Use a graphing utility to graph the function.Approximate the local maxima rounded to two decimal places, if
necessary. Approximate the local minima rounded to two decimal places, if necessary.
e) Determine the number of turning points on the graph.
f) Put all the information together, and connect the points with a smooth, continuous curve to obtain the graph of f.

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