Math

Math 1. For the function below, find the intervals of increase and decrease, and the intervals of concavity. y = x3 +2x2 – 4x + 1 2. Determine the absolute and local extreme values of each function on the given interval. a) f (x) = 2x3 – 3x2 – 12x + 2, – 3 x 3 b) f (x) = x3 + x , 0 x 10 3. Determine the angle between these two vectors below. = [–6, 3, 0] and = [7, 2, 4] 4. Write the parametric equations of a line perpendicular to 4x + 8y + 7=0 with the same x-intercept as [x, y] = [2, 7] + t [–10, 3]. 5. A plane is defined by the equation x – 4y + 2z – 16 = 0. a) Find two vectors parallel to the plane. b) Write the vector and parametric equations of the plane. 6. A certain computer that is purchased today depreciates in value according to the function V(t) = 900 e , V represents value, in dollars; t represents time, in years, a) What was the purchase price of the computer? b) What is its value after 1 year? c) How long will it take for the computer’s value to decrease to half of its original value? 7. If = [5, 8, 2] , = [–7, 3, 6] , determine × and • 8. Determine the equation for the tangent line to the functions. a) y = 2x2 – 1 at x = – 2 b) y = 2sinx + 4cosx at x = c) y = –3ex at x = ln3