I need help with both of this math problem.

Question 1:

Consider the function x) and its derivatives: 1 3:2 2320.32 3) fi($):m and fit\"): ($2+1)3 (a) [2 points] Find the critical numbers of at) and show your work tojustify. (b) [2 points] Find the open interva|(s) where f is decreasing and the open interva|(s) where f is increasing. Show your work tojustify your answer. (c) [2 points] Find the xcoordinate(s) ofall local minima off and all local maxima of f. Show your work to justify. (d) [4 points] Find the open intervals where f is concave up and the open intervals where f is concave down. Show your work to justify. (e) [2 points] Find the x coordinates of all inflection point(s) of f, and show your work to justify. A box with a rectangular base and no top is to be made to hold 2 litres (or 2000 m3 ). The length of the base is twice the width. The cost of the material to build the base is $2.25/cm2 and the cost for the sides is $1.50/cm2. What are the dimensions of the box that minimize the total cost? Justify your answer. Hint: Cost Function 0: 2.25x area of base | 1.5x area of four sides