There are 2 bonus questions. Each question is worth 10 points. Please show your work in details step by step in order to earn the grading points. Good Luck to You!

Curve Sketching

Sketch a graph of the following function by the guidelines: 1. = 4 3 6 2 24

a. Describe behaviors of y when x becomes very large positive and very large negative. (1 point)

b. Find the x-intercept points and y-intercept points. (1 point)

c. Find the first derivative of y. (1 point)

d. Find the critical points and max points and/or min points. (1 point)

e. Find the increasing intervals and the decreasing intervals. (1 point)

f. Find the second derivative of y. (1 point) g. Find the inflection points. (1 point)

h. Find the concave upward intervals and concave downward intervals. (1 point)

i. Draw the curve sketching. (2 points)

Related Rates

Gravel is being dumped from a conveyor belt at a rate of 25 ft^3 per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 18 feet high? (10 points) Please draw the picture of a right circular cone to mark the height h, the base diameter d, and the base radius r.