`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.
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`