4. _y=x(x+3), y': y=4x+9 3(x+3) 4x+18 9(x+3) a) For the function, find each of the following....

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4. _y=x(x+3), y': y=4x+9 3(x+3) 4x+18 9(x+3) a) For the function, find each of the following. (15 pts) x-intercept(s) y-intercept(s) critical values Intervals where the function is increasing Intervals where the function is decreasing Relative maximum(s) Relative minimum(s) Intervals where the function is concave up Intervals where the function is concave down Points of Inflection b) Below is a graph of the function. Use it to label the relative (local) minimum and maximum points as well as the inflection points. Be sure to give both x and y coordinates for each of these points. Round to 3 places after the decimal if necessary. (5 points) 10 -5 c) If the function is restricted to the interval [-4, 5], what would be the absolute maximum and absolute minimum values? (4 points) 7. The radius of a circular disk is given as 24-cm with a maximum error in measurement of 0.2-cm. (8 pts) a) Use differentials to estimate the maximum error in the calculated area of the circular disk. b) What is the percentage error? 8. Verify that the function satisfies the hypotheses of The Mean Value Theorem on the given interval. Then find all numbers c that satisfy the conclusion of The Mean Value Theorem. (8 pts) f(x)= [1,4] x+2' 4. _y=x(x+3), y': y=4x+9 3(x+3) 4x+18 9(x+3) a) For the function, find each of the following. (15 pts) x-intercept(s) y-intercept(s) critical values Intervals where the function is increasing Intervals where the function is decreasing Relative maximum(s) Relative minimum(s) Intervals where the function is concave up Intervals where the function is concave down Points of Inflection b) Below is a graph of the function. Use it to label the relative (local) minimum and maximum points as well as the inflection points. Be sure to give both x and y coordinates for each of these points. Round to 3 places after the decimal if necessary. (5 points) 10 -5 c) If the function is restricted to the interval [-4, 5], what would be the absolute maximum and absolute minimum values? (4 points) 7. The radius of a circular disk is given as 24-cm with a maximum error in measurement of 0.2-cm. (8 pts) a) Use differentials to estimate the maximum error in the calculated area of the circular disk. b) What is the percentage error? 8. Verify that the function satisfies the hypotheses of The Mean Value Theorem on the given interval. Then find all numbers c that satisfy the conclusion of The Mean Value Theorem. (8 pts) f(x)= [1,4] x+2'