- Determine the slope of the graph of at the point with -coordinate 1.
- Find the volume of the solid of revolution formed by rotating the region between the graph of and the interval about the -axis.
- To take this derivative, using logarithmic differentiation will be easier,
Then differentiating both sides we have,
So, to find the slope at the point with we evaluate,
- First, the integral to compute the volume of the solid of revolution is,
To evaluate this we use the partial fraction decomposition,
This gives us the equation
Evaluating at , , and we obtain
Therefore, we have