# Math Help - optimization problem

1. ## optimization problem

Suppose R is the region bounded by the curves y = any function f(x) and y = c, on the interval a to b. Find the value of c that minimizes the volume of the solid that is generated by revolving R about the line y = c.

2. ## Re: optimization problem

$V(c)=\int_a^b \pi[f(x)-c]^2 dx$
$\frac{dV}{dc}=\int_a^b 2\pi[f(x)-c](-1) dx$
$=-2\pi\int_a^b [f(x)-c] dx$
resolve dV/dt = 0, we get $c = \frac{\int_a^b f(x)dx}{b-a}$

3. ## Re: optimization problem

Where does the (-1) in step two come from?