Given f(x)=x^2-64/x^2-8x: 1) Find domain. Use interval notation. 2) State any y-intercept and x-intercept. (If an intercept doesn't exist state it and show why) 3) Show how to test symmetry with respect to Y-axis and with respect to Origin. (If a symmetry doesn't exist state it after steps)
Given f(x)=x^2-64/x^2-8x:
1) Find domain. Use interval notation.
2) State any y-intercept and x-intercept. (If an intercept doesn't exist state it and show why)
3) Show how to test symmetry with respect to Y-axis and with respect to Origin. (If a symmetry doesn't exist state it after steps)
4) Use limits to find vertical asymptote. (If it doesn't exist prove it with limits)
5) Use limits to find horizontal asymptote. (If it doesn't exist prove it with limits)
6) Find first derivative and show in which intervals the function decreases/increases.
7) State any local extrema. If none, state why.
8) If the second derivative is ?(?)=16/?^3. Show on which intervals the function concave upward/downward. Use interval notation.
9) State any inflection point. If none, state why.
10) Sketch graph of ?(?)f(x) . (Label: x-axis, y-axis, any asymptotes, any intercepts)
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