Need help whole page thank you.

Instructions: | 1. Showing work is required. Show all your work on Bluebook. No work no credit. 2. Please your answer on Bluebook. 3. Calculator (not phone calculator) is allowed. Problem 1. (10') Use the limit definition of derivative to find the derivative of the function: flz)=22" +3z4 Problem 2. (10) Find the derivative of the following functions: @@= 220 () o) = VEre(Ea) Problem 3. (10) Find the derivative y' = % of the function: y=z* Problem 4. (15') Using implicit differentiation, find the equation of the tangent line (in slope-intercept form) to the given curve at the given point: P -Tay+z25=9 at (0,3) Problem 5. (10') Consider the function y = v3z: a . Find the differential dy. b . Evaluate dy for = 6 and dz =03 Problem 6. (10') Sand pours from a chute and forms a conical pile whose height is always equal to its bas of 5 feet/hour. Find the rate of change of the volume ( diameter. The height of the pile increases at a rate the sand in the conical pile, when the height of the pile is 4 feet. Hini: V = zmr2h. Problem 7. (15) A boz with a square base and an open top must have a volume of 256 cubic inches. Fi the dimensions of the box that will minimize the amount of material used (the surface area). Problem 8. (20) For the function y = 23 322 1, use derivatives to: o . determine the intervals of increase and decrease. b . determine the local (relative) mazime and minima. . determine the intervals of concavity. ' d . determine the points of inflection. e . sketch the graph with the above information indicated on the graph