Math

 Differentiate the function with respect to . Explain your answer in a sentence by quoting a relevant theorem. When in doubt, sketch a graph of a given function.

(a)

(b)

(c)

(d)

(e)

(f)

 Differentiate the function with respect to :

(a)

(b)

(c)

(d) ,

(e) .

 Find: . (Note the problem was updated)

 Find where and are constants.

 The equation of motion of a particle is , where is measured in meters and is in seconds.

(a) Find the velocity () and acceleration () as functions of .

(b) Find the acceleration at time .

(c) Graph the position, velocity, and acceleration functions on the same screen. Then retrace the graphs on paper.

 Find an equation of the tangent line to the curve , parallel to the line . (Hint: What must be the slope of this tangent line?) Graph on the same screen , , and the tangent line .

 Find a second degree polynomial (a function ) such that , , and .