Math 16a worksheet 7 is the function fx -12x4 concave up

Question

MATH 16A WORKSHEET 7-

(1) Find all relative maxima and minima of the function f(x) = (1/3)x³ - (5/2)x² + 4x + 1 and indicate whether each point is a minimum or maximum.

(2) Is the function f(x) = -(1/2)x⁴ concave up or down at x = 0?

(3) Find the quadratic function f(x) = ax² + bx + c that goes through (-1, 6) and has a local minimum at (2, 1).

(4) Find the minimum of Q = x² + y² if x + y = 6. Is there an absolute maximum?

(5) Find two positive numbers x and y whose sum is 13 and whose product is as large as possible.