`f(x) = ((x + 4)(x - 3)^2)/((x^4)(x - 1))` Sketch the graph by hand using asymptotes and intercepts, but not derivatives. Then use your sketch as a guide to producing graphs (with a graphing device) that display the major features of the curve. Use these graphs to estimate the maximum and minimum values.
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Vertical asymptotes are real zeros of the denominator of the function.
`x=0 , x=1`
Vertical asymptotes are at x=0 and x=1
Degree of numerator =3``
Degree of denominator=5
Since degree of denominator is `>` degree of numerator,
so Horizontal asymptote is the x-axis. HA is y=0
See the attached image and links. f(x) is plotted in several ranges to have clarity.
From the graph f has no y intercept , x intercepts x=-4 , 3
Function has three maximum values,
f(`~~` -5.5)`~~` 0.02
f(`~~` 5) `~~` 0.015
f(`~~` 0.825) `~~` -275
Function has one Minimum value
Minimum at `-oo` and maximum at `oo`
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