11. Revenue/Cost/Profit Given the revenue and cost functions R=50x - 0.4r and C 5x+ 15 (in dollars), where x %3D is the daily production (and sales), find the following when 40 units are produced daily and the rate of change of production is 10 units per day. (a) The rate of change of revenue with respect to time (b) The rate of change of cost with respect to time (c) The rate of change of profit with respect to time

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4. Find all points on the curve y = -x³ +-x* + 6x² where the tangent line is horizontal. 5. Find all x-values in which your function has horizontal tangent lines, f(x) = 2 sin x + x. given 0s x < 2n. 6. Find the equation of the line tangent to the graph of xy + y² = 4 at x = 3. 7. A ball is thrown up from the top of a 48-foot tower with initial velocity of 32 feet per second. Given that the position of the ball at any time t is given bys(t) = -16t2 + 32t + 48, answer the following questions. a. What is the average velocity for the first five seconds the ball is in the air? b. What is the instantaneous velocity 1 seconds after the ball is thrown? C. What is the height of the ball 1 seconds after the ball is thrown? d. At what time does the ball reach its maximum height? e. What is the maximum height of the ball? f. At what time is the velocity of the ball 10 sec g. What is the velocity of the ball when it hits the ground? h. What is the velocity of the ball when it reaches its maximum…

x + 2 For the function y = at (3, 1), find the following. (Give exact answers. Do not round x + 8 (a) the slope of the tangent line 0.4545 Enter an exact value instead of a rounded value. (b) the instantaneous rate of change of the function 0.4545 Enter an exact value instead of a rounded value.