Question 435111
1)Given f(X)= x³-5x:
a)Use the leading coefficient test to determine the end result behavior of the graph of f(x)
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As x goes to -inf, x^3 goes to -inf, so f(X) goes to -inf.
As x goes to +inf, x^3 goes to +inf, so f(X) goes to +inf.
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b)Find the zeros of f(x)
Solve x^3-5x = 0
x(x^2-5) = 0
x(x-sqrt(5))(x+sqrt(5)) = 0
x = 0 or -sqrt(5) or +sqrt(5)
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c)Demonstrate the remaining steps necessary for graphing this function and use this information to graph f(x).
y-intercept = 0^3-5*0 = 0
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Other analysis depends on what your text requires.
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{{{graph(400,300,-10,10,-10,10,x^3-5x)}}}
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Cheers,
Stan H.
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