Consider the function f(x) = x2 - x - 30. Use a graphing utility to graph f, the secant line, and the tangent line. (a) Find the equation of the secant line joining the points (-4, -10), and (6, 0). x-y - 6=0 (b) Use the mean value theorem to determine a point c in the interval (-4, 6) such that the tangent line at c is parallel to the secant line. C = 1 (c) Find the equation of the tangent line through c. x-y - 31 X Need Help? Read ItDetermine whether the Mean Value theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = V2- x, [-23, 2] Yes, the Mean Value theorem can be applied. No, f is not continuous on [a, b]. No, f is not differentiable on (a, b). None of the above. If the Mean Value theorem can be applied, find all values of c in the open interval (a, b) such that f'(c) = _. (Enter your answers as a comma-separated list. If the Mean Value theorem cannot be applied, enter NA.) b - a Need Help? Read ItThe height of a ball t seconds after it is thrown upward from a height of 6 feet and with an initial velocity of 80 feet per second is f(t) = 16t? + 80t + 6. (a) Verify that f(2) = f(3). f(2) = ft f(3) ft (b) According to Rolle's theorem, what must be the velocity (in ft/sec) at some time in the interval (2, 3)? 0 ft/sec Find that time (in seconds). t= Ss Determine whether Rolle's theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) fx) = (x - 9)(x + 3)?, [-3, 9] Yes, Rolle's theorem can be applied. No, because f is not continuous on the closed interval [a, b]. No, because f is not differentiable in the open interval (a, b). No, because f(a) # f(b). S If Rolle's theorem can be applied, find all values of c in the open interval (a, b) such that f'(c) = 0. (Enter your answers as a comma-separated list. If Rolle's theorem cannot be applied, enter NA.) c=|3 x Need Help? Read It Determine whether Rolle's theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = (x 1) - 3) 8), [1, 8] Yes, Rolle's theorem can be applied. No, because f is not continuous on the closed interval [a, b]. No, because f is not differentiable on the open interval (a, b). No, because f(a) # f(b). So If Rolle's theorem can be applied, find all values of c in the open interval (a, b) such that f'(c) = 0. (Enter your answers as a comma-separated list. If Rolle's theorem cannot be applied, enter NA.) 183-J/9 18+V9 1 2 1 a Need Help? Read It Watch It Consider the graph of the function f(x) = =x? +7. (a) Find the equation of the secant line joining the points (1, 6) and (2, 3). (Enter your answer in terms of x and y.) (b) Use the mean value theorem to determine a point c in the interval (1, 2) such that the tangent line at c is parallel to the secant line. c= 1/12 3 (c) Find the equation of the tangent line through c. (Enter your answer in terms of x and y.) |