In Exercises 17-22, find the slope of the tangent line to the graph of the function at the given point, and determine an equation of the tangent line.M 17. f(x)=2x+7 at (2, 11) erg griwollot ST YATZ 18. f(x) = 3x + 4 at (-1, 7) B eqz-signia s ni beaubong Dodaq at idu ni 19. f(x) = 3x at (1, 3) or to asqola odi gnituqm - boow sdt doidw is 5181 or similes 20. f(x) = 3x = x at (-2, -10) ay to saints at the 10 ang ent store had all town. The months) is evenue of the en by g(t) ons by giving ok place. dobou A d.s store is tore is akes that ng at the slope of any point. he an the 24. Let f(x) = x + 6x. a. Find the derivative f' of f. b. Find the point on the graph of where the tangent line C. to the curve is horizontal. Hint: Find the value of x for which f'(x) = 0. Sketch the graph of and the tangent line to the curve at the point found in part (b). 25. Let f(x) = x - 2x + 1. a. Find the derivative f' of f. b. Find the point on the graph of where the tangent line to the curve is horizontal. c. Sketch the graph of f and the at the point found in part (b). 31. V tangent line to the curve 32. d. What is the rate of change of f at this point? 26. Let f(x) = 1 x-1 a. Find the derivative f' of f. b. Find an equation of the tangent line to the curve at the point (-1, -1). c. Sketch the graph of f and the tangent line to the curve at (1, ). 27. Let y = f(x) = x + x. a. Find the average rate of change of y with respect to x in the interval from x = 2 to x = 3, from x = 2 to x = 2.5, and from x = 2 to x = 2.1. b. Find the (instantaneous) rate of change of y at x = 2. c. Compare the results obtained in part (a) with the result of part (b). 28. Let y = f(x) = x - 4x. a. Find the average rate of change of y with respect to x in the interval from x = 3 to x = 4, from x = 3 to x = 3.5, and from x = 3 to x = 3.1. b. Find the (instantaneous) rate of change of y at x = 3. c. Compare the results obtained in part (a) with the result of part (b). (1)z 29. VELOCITY OF A CAR Suppose the distance s (in feet) covered by a car moving along a straight road after t sec is given by the function s = f(t) = 2t + 48t. a. Calculate the average velocity of the car over the time intervals [20, 21], [20, 20.1], and [20, 20.01]. b. Calculate the (instantaneous) velocity of the car when 29200 X t = 20. c. Compare the results of part (a) with the result of part (b). 30. VELOCITY OF A BALL THROWN INTO THE AIR A ball is thrown straight up with an initial velocity of 128 ft/sec, so that its height (in feet) after t sec is given by s(t) = 128t - 16t. a. What is the average velocity of the ball over the time intervals [2, 3], [2, 2.5], and [2, 2.1]? b. What is the instantaneous velocity at time t = 2? c. What is the instantaneous velocity at time t = 5? Is the ball rising or falling at this time? d. When will the ball hit the ground? 33 3