Problem 1. (10 points) The point P(5,36) lies on the curve y : 1:3 +x 4 6. If Q is the point (1,12 +x +6), nd the slope of the secant line PQ for the following values of x. lfx : 5.1, the slope of PQ is: and ifx : 5.01, the slope of PQ is: and ifx : 4.9, the slope of PQ is: and ifx : 4.99, the slope of PQ is: Based on the above results, guess the slope of the tangent line to the curve at P(5. 36). Problem 2. (10 points) A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 49 ft/s. Its height in feet after t seconds is given by _v : 49: 10:2. A. Find the average velocity for the time period beginning whenr : 1 and lasting .01 s: .005 s: .002 s: .001 s: NOTE: For the above answers, you may have to enter 6 or 7 signicant digits if you are using a calculator. B. Estimate the instantaneous velocity when t = 1. Answer: Problem 3. (3 points) A. For the function f (x) : 2x2 - 8x 2 nd mm :, the slope of the secant line between the values x1 and x3. ((Round to 6 decimal places.) a. no : 2 and X2 : 3, mm. : 13.x] : 2 and x; : 2.1, mm : C. no : 2 and X2 : 2.01, mm. :_ B. Use the answers from parts a,b,c to estimate mm", the slope of the tangent line to f at point x : 2. (The answer should be an integer). mum :_ Problem 5. [6 points] Using the graph of g(x) below. answer the following questions. a 1,9 -5 .5. 3) Where is g(x) > 0 '? 7 (Enter an interval) b) Where is g(x] O ? _ (Enter an interval) e) Where is g'(x}