Given xy + y = ey + sin (xy), find y' What is the difference between a local maximum and an absolute maximum? P Find the absolute extreme values (maximum and minimum) for the function f(x) = 4x - 3x on the interval [-5,2]. IYOW What does the sign of the derivative f'(a) tell you about f(x) at x = a. P Find the interval(s) over which f(x) = 4x - 3x is increasing by finding where f'(x) > 0. IYOW If g(x) has one local minimum, at x = 4, what can you say about f'(2)? What about f'(7)? If f'(x) (the derivative of f(x)) tells you about the rate of change of f(x), what does f"(x) (the derivative of f'(x)) tell you about f'(x)? Given g(x) = 4x - 3x, find g"(x). Suppose that you have 40 feet of fencing you want to use to enclose a region in your garden. What shape do you think that the region should be in order to maximize the area of it? What is the equation of the line tangent to f(x) at x = a?