2. Find the equation of the line tangent to

at

\(\displaystyle y=\frac{5}{13}x+\)\(\displaystyle \frac{21}{13}\)

ok

3. Find the point P on the graph of

closest to the point

How do I find the point from here? Do I plug 10 in for x?

how about taking a derivative?

4. Calculate the surface area of revolution of

about the x-axis over

=

Here is my work, please let me know where I went wrong.

\(\displaystyle y=(4-x^\frac{2}{3})^\frac{3}{2}\)

\(\displaystyle y'=-x^\frac{-1}{3}(4-x^\frac{2}{3})^\frac{1}{2}\)

\(\displaystyle (y')^2+1\rightarrow 1+(4-x^\frac{2}{3})^\frac{1}{2})^2=1+\frac{4-x^\frac{2}{3}}{x^\frac{2}{3}}=\frac{x^\frac{2}{3}}{x^\frac{2}{3}}+\frac{4-x^\frac{2}{3}}{x^\frac{2}{3}}=\frac{4}{x^\frac{2}{3}}\)

\(\displaystyle u=4-x^\frac{2}{3}\)

\(\displaystyle du=-\frac{2}{3}x^{-\frac{1}{3}}dx\)

\(\displaystyle -3du=2x^{-\frac{1}{3}}\)

\(\displaystyle 2\pi\int_{2}^{3}u^{\frac{3}{2}}(-3)du=-6\pi\frac{2}{5}u^{\frac{5}{2}}\Bigg|_{2}^{3}=-\frac{12\pi}{5}(4-x^{\frac{2}{3}})^{\frac{5}{2}}\Bigg|_{2}^{3}\)