Directions: Show the appropriate work for each question for full credit. No credit for answer only. 1. [5] Find the derivatives for the given functions. Simplify as much as possible. a) y = -In (1- 4x2) b ) f(x) = -4.V10x3 - 7x2 +e b ) g (x ) = (3x3 - 7)3 In (5x4 + 1) 2. [2] Find f' (x) and find the values of x where the tangent line is horizontal. f (x) = X (6x-7)9 3. [2] Let f(x) = -3ex-9x+5. Find the equation of the line tangent to the graph of f (x) at x = 1. Leave answer in exact form.4. [4] Let f(x) = -x3 - 2x2 + 4x + 2. Answer the following questions. Page 4 of 7 a) f (x) is increasing on: and f (x) is decreasing on: b) f (x) is concave upward: and f(x) is concave downward: c) f (x) has a local maximum at x = and f (x) has a local minimum at x = d) Does f (x) have an inflection point? If so, give the coordinates of the inflection point. Show work here (must include 1st derivative and 2nd derivative sign charts): x tooth 5. [3] Use the price-demand equation to find the values of p for which demand is elastic and the values for which demand is inelastic. Assume that price and demand are both positive. Leave answer in simplified radical form. x =f(p) = 3380 - 5p2 (Use interval notation) The values of p for which demand is elastic are (Use interval notation) The values of p for which demand is inelastic are6. [2] A boat is being pulled toward a dock as shown in the figure to the right. If the rope is being Page 5 of 7 pulled in at the rate of 4 feet per second, how fast is the distance between the dock and the boat decreasing when it is 2 feet from the dock? Show set up and steps. Leave answer in exact form. Rope 7. [2] A retail store estimates that weekly sales s and weekly advertising costs x (both in dollars) are related by S(t) = 40,000 - 20,000e-0.0004x . The current weekly advertising costs are $2,500 and these costs are increasing at a rate of $600 per week. Find the current rate of change of sales. Round to the nearest dollar. 8. [2] A commercial cherry grower estimates from past records that if 30 trees are planted per acre, then each tree will yield an average of 50 pounds of cherries per season. If, for each additional tree planted per acre (up to 21 additional trees), the average yield per tree is reduced by 1 pound, how many trees should be planted per acre to obtain the maximum yield per acre? What is the maximum yield