7. [-/2 Points] DETAILS TANAPCALC10 2.6.020.MI. Find the slope of the tangent line to the graph of the function at the given point. f(x) = 5x - 2x2 at (-2, -18) m = Determine an equation of the tangent line. y Need Help? Read It Master It 8. [-/4 Points] DETAILS TANAPCALC10 2.6.028.MI. Let f be defined as follows. y = f(x) = x2 - 11x (a) Find the average rate of change of y with respect to x in the following intervals. from x = 6 to x = 7 from x = 6 to x = 6.5 from x = 6 to x = 6.1 (b) Find the (instantaneous) rate of change of y at x = 6.9. [/7 Points] TANAPCALC1O 2.6.030. ASKYOUR TEACHER PRACTICE ANOTHER Velocity of a Ball Thrown into the Air The position function of an object moving along a straight line is given by s = f(t). The average velocity of the object over the time interval [a, b] is the average rate of change of fever [a, b]; its (instantaneous) velocity at t = a is the rate of change of fat a. A ball is thrown straight up with an initial velocity of 112 ft/sec, so that its height (in feet) after L' sec is given by S = ftt) = 112t 161'2. (a) What is the average velocity of the ball over the following time intervals? [2, 3] ft/sec [2, 25] ft/sec [2; 2-1] ft/sec (b) What is the instantaneous velocity at time t = 2? ft/sec (c) What is the instantaneous velocity at time t = 6? ft/sec Is the ball rising or falling at this time? O rising O falling (d) when will the ball hit the ground