Analyze the relative and absolute extrema for the function below by completing the steps indicated.f(x)=x33x2-5x5x-13Manually find the derivative, f'(x). Don't use any technology help in this part. Show all work. List all derivative rules used. Do NOT simplify your final answer, f(x) is in uv form apply quotient rule for derivativef'(x)=(5x-13)(3x26x-5)-(x33x2-5x)(5xln(5))(5x-13)2f'(x)=Find the critical numbers for this function. Show all work and specify any kind of technology you used. State how you set things up in your device. Round numbers to 3 decimal points.CN where f'(x) DNE:CN where f'(x)=0;Make a sign chart for f'(x). Correctly label your axis-Clnssify the relative extrema based on the sign chart above. Round numbers to 3 decimal points. Write answers in the (x,y)-coordinate form:Relative max(cs)Relative min(s)5. Use the table of valucs to find and classify the absolute extrema of f(x) on the interval -2,2. Round numbers to 3 decimal points. If there is no such extrema, put NONE and briefly explain why.Write answers in the (x,y)-coordinate form:Absolute max Absolute min