1. vnicn of the following functions have a derivative of zero (0)? a. f(x) = 9.8 b. f(x) = 11 C. f(x) = -4+x d. f(x) = =x e. f(x) = V7 f . f (x ) = x g. f(x) = 3 h. f ( x ) = - 2.8n 2. Use the Power Rule to determine the derivative for each of the following. a . f ( x ) = x b. f (x) = =x C. f(x) = x5 d. f (x ) = -3x4 e f(x) = 1.5x3 f . f (x) = Vx3 g. f ( x ) = = h . f ( x ) = Use the Product Rule to differentiate each of the following. f(x) = (x2 - 2x)(3x + 1) b. f(x) = (1-x3) (- x2 + 2) C. f(x) = (3x - 1)(2x + 5) f (x) = (-x2 + x)(5x2 - 1) e . f(x) = (2x -x2) (7x + 4) d. f ( x ) = (-5x3 + x) (-x+2) 4. Determine the equation of the tangent to each curve at the indicated value. f(x) = -4.9t2, t = 3.5 b f (x ) = (x2 - 3) (x2 + 1), x = -4 h(x) = (x4+4)(2x2 -6), x = -1 d. y = 2 X = -2 5 . The gas tank of a parked pickup truck develops a leak. The amount, V, in litres, of gas remaining in the tank after t hours can by modelled by the function V = 60 (2 - 5) , Osts 10 a. How much gas was in the tank when the leak developed? How fast is the gas leaking from the tank at t = 7 h? How fast was the gas leaking from the tank when there is 15 L of gas in the tank? 6. The cost, C, in dollars, of producing x frozen fruit yogurt bars can be modelled by the function C(x) = 3450 + 4.5x - 0.0001x2, 0 s x $ 5000. The revenue from selling x yogurt bars is R(x) 3.25x. a Determine the cost of producing 1000 frozen fruit yogurt bars. What is the revenue generated from selling this many bars Compare the values of C'(1000) and C'(3000). What information do these values provide? When is C'(x) = 0? Explain why this is impossible. Determine R'(x). What does this value represent? e . The profit function, P(x) is the difference between the revenue and cost functions. Determine an equation for P(x). f . When the profit function positive? When is it negative? What important information does this provide the owners