Exam 3: Differentiation

Suppose the position function for a free-falling object on a certain planet is given by .A silver coin is dropped from the top of a building that is 1380 feet tall.Find velocity of the coin at impact.Round your answer to the three decimal places. ​

Find if . ​

Use Newton's Method to approximate the zero(s)of the function accurate to three decimal places. ​

Find in terms of x and y given that . ​

Use the Quotient Rule to differentiate the function . ​

A man 6 feet tall walks at a rate of 13 feet per second away from a light that is 15 feet above the ground (see figure).When he is 5 feet from the base of the light,at what rate is the length of his shadow changing? ​ ​

Find if . ​

Find an equation of the tangent line to the graph of f at the given point. ​ ​ at ​​

Find the derivative of the function by the limit process. ​​

​How fast is the area of the isosceles triangle increasing when the radius is 6 cm? Include units in your answer.Round your answer to 3 decimal places.

Find the derivative of the function . ​

A projectile is shot upwards from the surface of the earth with an initial velocity of 136 meters per second.The position function is . ​ What is its velocity after 6 seconds? ​

Find if . ​

The graph of the function f is given below.Select the graph of f´. ​ ​ ​

Use implicit differentiation to find . ​ ​

Find an equation of the line that is tangent to the graph of f and parallel to the given line. ​ ,

Identify the graph which has the following characteristics. ​ Graph 1 Graph 2 Graph 3 Graph 4

Find the points at which the graph of the equation has a vertical or horizontal tangent line. ​ ​

Find by implicit differentiation. ​ ​​

The displacement from equilibrium of an object in harmonic motion on the end of a spring is where y is measured in feet and t is the time in seconds.Determine the position of the object when .Round your answer to two decimal places. ​