Sketch the graph of a single function f(x) that satisfies all of the following con-ditions. Find critical numbers for f'(x) and f''(x) and show sign charts for bothfunctions. Indicate the intervals where f(x)is increasing, decreasing, concave upand concave down. Give x-coordinates of all local maxima, local minima, andinflection points and label them. Show asymptotes using dashed lines.(i)f(x)is defined and continuous for all real numbers except atx=0 and x=2(ii)f'(x)=-1x2-2x(iii)f''(x)=2(x-1)x2(x-2)2(iv)limx-f(x)=0(v)limxf(x)=0(vi)limx0f(x)=-(vii)limx2f(x)=(viii)f(1)=0