Weekly Assignment 2

1. Function analysis

Let f(x)=(e^(2x))-3x.

Find an equation for the tangent line to y=f(x) when x=0.

Find any critical numbers for f(x) and determine if each produces a local maximum point, a local minimum point, or neither. Show your work (other than pointing to a graph) in determining this information.

2. Area and Volume

Let R be the region in the plane bounded by y=(1/x), y=(1/(Sqrt[x])), and x=4.

Sketch the planar region.

Find the area of R.

Find the volume of the solid of revolution obtained by rotating R about the x axis.