Given (10 pts) Show your work in the upload submission.  In…

Given (10 pts) Show your work in the upload submission.  Input the final answer in the given space below.  (1 pt) Find the derivative of the function using the definition of derivative. (1 pt) Find an equation of the tangent line (in slope-intercept form) to the graph of at x=-1. (1 pt) Find the point(s), as an ordered pair, on the graph of at which the tangent line is horizontal, if any.

A boat travels north from a dock at 12 mph. Three hours late…

A boat travels north from a dock at 12 mph. Three hours later, a second boat leaves the same dock, sailing west at 16 mph. How fast are the boats moving apart when the second boat has been sailing for 2 hours? Round the answer to the nearest hundredth. Clearly show your work in the upload submission: (2 pts) Draw a diagram and label all the known values and unknown values (e.g., x, y, z, etc) (4 pts) Show your calculations in the upload submission. Make sure to clearly show how you form the function that you use to obtain your answer. (2 pts) Enter your answers in the space below, using the correct units when necessary. Use ^ to denote exponents, for example, type x^3 for x³. Round your answer to two decimal places. The function you use to find the rate [a] The rate at which the boats are moving apart is [b] when the second boat has been sailing for 2 hours.

The height (in meters) of a projectile shot vertically upwar…

The height (in meters) of a projectile shot vertically upward from a point 3 m above ground level with an initial velocity of 23.5 m/s is after t seconds. (11 pts) Show your work in the upload submission. Input the final answer in the given space below. (Round your answer to two decimal places) (1 pt) The velocity after 4 seconds is [a]. (1 pt) The time the projectile reaches its maximum height is [b]. (1 pt) The maximum height is [c]. (1 pt) The time it hits the ground is [d]. (1 pt) The velocity when it hits the ground is [e].