1. The graphs of the function f (given in blue) and g (given in red) are plotted above. Suppose that u (x) = f (x) g (x) and v (x) = f (x) / g (x) . Find each of the following:
2. Find an equation for the line tangent to the graph of
f (x) = -3xex
at the point (a, f(a)) for a = 2.
3. The motion of a spring that is subject to a frictional force or a damping force (such as a shock absorber on a car) is often modeled by the product of an exponential function and a sine or cosine function. Suppose the equation of motion of a point on such a spring is
s (t) = 5e-1.4t sin (2πt)
where s is measured in centimeters and t is measured in seconds. Find the velocity of the point after t seconds.