3. Determine the absolute extrema of each function on the given interval. Illustrate your results by sketching the graph of each function. a. f(x) = x - 4x + 3, 05x=3 b. f ( x) = (x - 2)3, 0 = x = 2 c. f(x) = > - 3x, -15x=3 d. f(x) = x3 - 3x-, x=[-2, 1] e. f(x) = 2x3 - 3x2 - 12x + 1, xe[-2, 0] f. f(x) = = x2 + 6x, xE [0, 4]1. Determine the points at which f'(x) = 0 for each of the following functions: a. f(x) = x3 + 6x- + 1 c. f(x) = (2x - 1)-(x2 - 9) 5.x b. f(x) = Vx2 + 4 d. f(x) = 2 + 1C.3. Evaluate lim f(x) and lim f(x), using the symbol "co" when appropriat 1-+00 2x + 3 -5x- + 3x a. f(x) = c. f(x) = X - 1 2x2 - 5 5.x2 - 3 2x5 - 3x3 + 5 b. f(x) = d. f(x) = x= + 2 3.x* + 5.x - 42. Determine the critical points for each function, and use the second derivative test to decide if the point is a local maximum, a local minimum, or neither. a. y= x - 6x2 - 15x + 10 c. s=1+1 25 b. y = 12 + 48 d. y = (x - 3)3 +84. Use the algorithm for curve sketching to sketch the following: a. y = x - 9x2 + 15x + 30 f. f(X) = 2 - 4x b. f(x) = - 4x3 + 18x- + 3 6x2 - 2 g. )= x+3 C. y = 3 + (x + 2)2 h. f(x) = x2 - 4 d. f(x) = x4 - 4x3 - 8x- + 48x x2 - 3x + 6 i. V= x- 1 2x e. V= j. f(x) = (x - 4) x2 - 25 5. Verify your results for question 4 using graphing technology