Q1:

Find the equation of the line tangent to the graph of fat (3, -1), where f is given by f(x) = 4x3 13x2 + 8. Use y as the dependent variable when you write your equation. E Let p(x) = x3 - 14x2 + 9x + 74 . Compute p '(x) and use it to find all values of x for which p '(x) = 0. X= (smaller value) X = (larger value)At a time t seconds after it is thrown up in the air, a tomato is at a height of f(t) = -4.9t2 + 25t + 6 meters. Give all answers below to two decimal places. (a) Find the average velocity of the tomato during the rst 1.5 seconds? (b) Find the instantaneous velocity of the tomato at t = 1.5. The value of a particular item can be modeled by P(t) = Po(a)t where P is in dollars and t is the number of years since the item was purchased. Suppose the value of the item increases 8% each year and the item was purchased for $20. (a) Write a formula for P(t) using the general exponential model. P0) = (b) How fast is the value of the item increasing when t = 5 years? Round your answer to two decimal places. dollars/year