Find the derivative. d dt dx -4x (Give an exact answer. Use symbolic notation and fractions where needed.), Consider the function. f(X) = x2 Calculate the average value of f on the interval [2, 7]. Give an exact answer. Determine c such that the average value of the function is equal to f (c). Give an exact answer with no radicals in the denominator. For the integral f (5x2 + 6) dx, find all numbers u guaranteed by the Mean Value Theorem for Integrals. (Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list.) u =Find the particular function y given that dy = x - 4x x + 6, when x = 1, y = 4 dx (Use symbolic notation and fractions where needed.)The acceleration of an object in rectilinear motion is given. Find the position function 5 = s(t) of the object under the given initial conditions. a(t) = et m/sz. 3(0) = 0 m, um) = 5 m/s (Express numbers in exact form, Use symbolic notation and fractions where needed.) A ball is thrown straight up from the ground level, with an initial velocity of 19.6 m/s. How high is the ball thrown? Assume the acceleration due to gravity is 9.8 m/sZ. (Use decimal notation. Give your answer to one decimal place.) How long will it take the ball to return to the ground level? (Give your answer as a whole or exact number.)