2a. 3a. run-mow Each derivative represents the first principles definition for some function f(x). State the function. .r _ . 3[x+h) 3:: r _ . (x+h)2 x2 f (x) _ i113}: h b' f (I) #53; h . 3 _ 3 . h)2 _ X2 .r = 1 4(x-l-h) 4x d r = 61 {x+ f (I) '33; h f (1:) Film h s 5 . ' ' . V): + n J27: J = 1: h r i' = f 0') L133: h f' f (x) #33) h Use the First Principle Method to determine the derivative of f(x) = 7 )8. What slope of the tangent at x = 6? Write the equation of the line for the tangent. Use the First Principle Method to determine the derivative of fix) 2 (2x 1F. Hint: expand the binomial first. What slope of the tangent at x z 6? Write the equation of the line for the tangent. 1 Use the First Principle Method to determine the derivative of fix) = x2. The height of a soccer ball after it is kicked into the air is given by hlt) = 4.1%2 + 3.5t + 1, where h is the height, in meters, and t is the time, in seconds. Use the First Principle Method to determine the rate of change of the height ofthe soccer ball at time t. Determine the rate of change ofthe height of the soccer ball at 0.5 5. When does the ball momentarily stop? What is the height of the hall at this time. Write your own equation in the form v = alx h)2 + k, where a, h, and k cannot equal zero {0). Use the First Principle Method to determine the rate of change. Select a value of x then calculate the slope of the tangent. Write the equation of the of the line ofthe tangent