MAT237Y1 Lecture Notes - Asymptote, Maxima And Minima
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Example: let"s graph another polynomial before going on to bigger and better things. Let g(x) = x2(x 1)2(x + 1)3. So, the y-intercept is at the origin. lim x lim x g(x) = + g(x) = . Set this equal to zero and x = 0, 1, 1, points. These are our critical f (x) = x(x 1)(x + 1)2(7x2 x 2) And that"s zero when x = 1, . 71, . 22, . 36, . 86. Now if we go ahead and do the rst derivative test at x = 1, then we"ll get pos to pos, so it"s neither a max nor a min. Also, both 0 and 1 had multiplicities of 2 and so both touched, but did not cross the x-axis, while being tangent to the x-axis at those points, plus the concavity didn"t change! Okay, now it"s time to deal with graphing rational functions. Recall that a rational function is the quotient of two polynomials.
