(20 points) Sketch the graph of a single function f(x) which satisfies all of the following conditions. Label all local maxima and minima, intervals of increase and decrease, points of inflection, concavity, and asymptotes.(i)f(x) is defined for all real numbers(i)f'(x)=-3(x2-3)2(x21)(iii)f''(x)=-12x(x21)2(iv)f(0)=0(v)f(3)~~3(vi)f(-3)~~-3(vii)limxf(x)=-(viii)limx-f(x)=4. Submit it here. Use the Canvas App to submit the PDFMacBook Proesc."%29582t3 ta*1235^57abZXv(20 points) Sketch the graph of a single function f(x) which satisfies all of the following conditions. Label all local maxima and minima, intervals of increase and decrease, points of inflection, concavity, and asymptotes.(i)f(x) is defined for all real numbers(i)f'(x)=-3(x2-3)2(x21)(iii)f''(x)=-12x(x21)2(iv)f(0)=0(v)f(3)~~3(vi)f(-3)~~-3(vii)limxf(x)=-(viii)limx-f(x)=4. Submit it here. Use the Canvas App to submit the PDFMacBook Proesc."%29582t3 ta*1235^57abZXv(20 points) Sketch the graph of a single function f(x) which satisfies all of the following conditions. Label all local maxima and minima, intervals of increase and decrease, points of inflection, concavity, and asymptotes.(i)f(x) is defined for all real numbers(i)f'(x)=-3(x2-3)2(x21)(iii)f''(x)=-12x(x21)2(iv)f(0)=0(v)f(3)~~3(vi)f(-3)~~-3(vii)limxf(x)=-(viii)limx-f(x)=4. Submit it here. Use the Canvas App to submit the PDFMacBook Proesc."%29582t3 ta*1235^57abZXv(20 points) Sketch the graph of a single function f(x) which satisfies all of the following conditions. Label all local maxima and minima, intervals of increase and decrease, points of inflection, concavity, and asymptotes.(i)f(x) is defined for all real numbers(i)f'(x)=-3(x2-3)2(x21)(iii)f''(x)=-12x(x21)2(iv)f(0)=0(v)f(3)~~3(vi)f(-3)~~-3(vii)limxf(x)=-(viii)limx-f(x)=4. Submit it here. Use the Canvas App to submit the PDFMacBook Proesc."%29582t3 ta*1235^57abZXv(20 points) Given the following information for a function f(x).(i)f(x) is defined for all real numbers(ii)f'(x)=9(x2-4)(x24)2(iii)f''(x)=-18x(x2-12)(x24)3(iv)f(0)=0(v)limxf(x)=0(vi)limx-f(x)=0(vii) The function has a local maximum value of 2.25.Find(a) All intervals on which f(x) is increasing or decreasing.(b)x-value(s) of all local (relative) extrema.(c) All intervals where f(x) is concave up or concave down.(d)x-value(s) of all inflection points.(e) Sketch the graph of f(x). Label all asymptotes, local extrema, and inflection points.4.(20 points) Sketch the graph of a single function f(x) that satisfies all of4. Subm