Question: [8 marks]Draw a single graph of the function g(x)so that each of the following is true:the domain ofg(x)is{xinR|x-1,x2}limx-1-g(x);limx-1+g(x)-limx2-g(x)-;limx2+g(x)-limx-g(x)=0;limxg(x)=0g'(0)=0;g'(4)=0;g''(6)=0g'(x)>0on the intervals (-,-1),(-1,0),(2,4)g'(x) <0on the intervals (0,2),(4,)g''(x)>0on
[8 marks]Draw a single graph of the function g(x)so that each of the following is true:the domain ofg(x)is{xinR|x-1,x2}limx-1-g(x);limx-1+g(x)-limx2-g(x)-;limx2+g(x)-limx-g(x)=0;limxg(x)=0g'(0)=0;g'(4)=0;g''(6)=0g'(x)>0on the intervals (-,-1),(-1,0),(2,4)g'(x)<0on the intervals (0,2),(4,)g''(x)>0on the intervals (-,-1),(6,)g''(x)<0on the intervals (-1,2),(2,6)g(0)=-2,g(4)=1,g(6)=13
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