Question

Suppose that f(x) = x4 + 12x3. (A) Use interval notation to indicate where f(x) is defined. If it is defined on more than one interval, enter the union of all intervals where f(x) is defined. Domain: (B) Find all intercepts. If there are no intercepts, enter None. If there are more than one, enter them separated by commas. x-intercept(s) = y-intercept(s) = (C) Find all critical values of f. If there are no critical values, enter None. If there are more than one, enter them separated by commas. Critical value(s) - (D) Use interval notation to indicate where f(x) is increasing or decreasing. If there are more than one interval, enter the union of all intervals. If the answer is the empty set, enter {}. Increasing: Decreasing: (E) Find the x-coordinates of all local maxima and minima off. If there are no local maxima, enter None. If there are more than one, enter them separated by commas. Local maxima at x = Local minima at x = (F) Use interval notation to indicate where f(x)is concave up or down. Concave up: Concave down: (G) Find all inflection points off. If there are no inflection points, enter None. If there are more than one, enter them separated by commas. Inflection point(s) at x = (H) Find all asymptotes of f. If there are no asymptotes, enter None. If there are more than one, enter them separated by commas. Horizontal asymptote(s): y = Vertical asymptote(s): x =

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Answer 1

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