Let f(x)={-6x2+5x,x<0,3x2-3,x0.a. First, determine the left and right-hand limitsoff(x)atx=0. Give an exact answer if a limitis a number.Otherwise, enter -orif a limitis infinite, or enter DNE if a limit does not exist in another way.Left: limx0-f(x)=limx0-|=|Right: limx0+f(x)=limx0+=b. Based on only Part a, what can you determine about the differentiability offatx=0?The limitoff(x)asx0 does not exist, sofis not continuous atx=0 and sois not differentiable there.The limitoff(x)asx0 exists, sof may be differentiable x=0, but we cannot conclude itisdifferentiable without more information.The limitoff(x)asx0 does not exist, sofis differentiable atx=0.The limitoff(x)asx0 does not exist, but f could still be differentiable atx=0.The left and right-hand limits exist, sofis differentiable atx=0.The left and right-hand limits are equal, sofis continuous atx=0 and therefore also differentiable there.