Hi! Good afternoon will you please help me answer and analyze these following problem set? Thank you so much. It is my reviewer for the exam.

1.

Find the Slope of the graph of the function at the given point. Find the Slope of the graph of the function at the given point. f(x) = 5x5 + 4x 5mm, (0, 0) Find an equation of the tangent line to the graph of fat the given point. f(x) = X+5 (i, 11) xl 2 Use the position function sft) = 16t' + vet + 50 for freefalling objects. A ball is thrown straight down from the top of a 7DOfoot building with an initial velocity of 40 feet per second. (a) Determine the position and velocity v(t) functions for the ball. : j (b) Determine the average velocity, in feet per second, on the interval [1, 3]. Em (C) Find the instantaneous velocities, in feet per second, when t = 1 and t = 3. m = EMS m) = Ems (d) Find the time, in seconds, required for the ball to reach ground level. [Round your answer to three decimal places.) :5 (e) Find the velocity of the ball, in feet per second, at impact. (Round your answer to one decimal place.) :Ws sft) v( t) Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. fix) = 2(5 X)2_ (7, 8) : f'U) Use the graph to estimate the open intervals on which the function is increasing or decreasing. Then find the open intervals analytically. (Enter your answers using interval notation.) y = - (x+ 2)2 increasing decreasing -5 -4 -3 X -2 - 1 1 - 1 -21 3 -5 -6 - 7Find the slope of the graph of the function at the given point. x) : V 1 X3: (2: 3) A sandbag is dropped from a balloon at a height of 60 meters when the angle of elevation to the sun is 30 (see figure). The position of the sandbag is s(t) = 60 4.9t2. Find the rate, in meters per second, at which the shadow of the sandbag is traveling along the ground when the sandbag is at a height of 24 meters. [Round your answer to two decimal places.) dx = E W... o't Use the graph of fto find the largest open interval on which fis increasing, and the largest open interval on which 1' is decreasing. (Enter your answers using interval notation.) Y (a) Find the largest open interval(s) on which I' is increasing. (Enter your answer as a commaseparated list of intervals}. (b) Find the largest open interval on which f is decreasing. S To estimate the height of a building, a stone is dropped from the top of the building into a pool of water at ground level. The splash is seen 6.9 seconds after the stone is dropped. What is the height of the building? Use the position function below for free-falling objects. (Round your answer to one decimal place.) 5m 2 4.9t2 + vet + s :m 0