Consider the curve given by the function f(x)=−3x^3/(x−2)(x+1)2. You are given that f′(x)=18x^2/(x−2)^2(x+1)^3andf′′(x)=−18x(3x^2−2x+4)/(x−2)^3(x+1)^4. Fill in the blanks. No justification is necessary. Answer "NONE" if the function does not display a feature listed. 

(a)[1 point] Domain of f 

(b)[1 point] x and y coordinates of x-intercept(s) of f 

(c)[1 point] x and y coordinates of y-intercept(s) of f 

(d)[1 point] Equation(s) of vertical asymptote(s) 

(e)[1 point] Equation(s) of horizontal asymptote(s) 

(f)[1 point] Critical number(s) of f 

(g)[1 point] Open interval

(s) where f is increasing 

(h)[1 point] Open interval

(s) where f is decreasing 

(i)[1 point] x and y coordinates of all local minimum(s) of f

(j)[1 point] x and y coordinates of all local maximum(s) of f 

(k)[1 point] Open interval(s) where f is concave up 

(l)[1 point] Open interval

(s) where f is concave down 

(m)[1 point] x and y coordinates of all inflection point(s) 

(n)[3 points] Use the above information to produce a sketch of the graph of y=f(x), labelling all maximums, minimums, inflection point(s), intercept(s), horizontal and vertical asymptote(s)

Answer rating: 100% (QA)

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