Homework Soursefind the local max and min values of f using both the first
find the local max and min values of f using both the first and second derivative tests.
f(x)=(x^2)/(x-1)
f(x)=(x^2)/(x-1)
Solution
f\'(x) = {(x-1) * (2x) -x^2 ( 1) } /(x-1)^2 ={ 2x^2 -2x -x^2} /(x-1)^2 = {x^2- 2x} / (x-1)^2 =0 =>x=0 or 2 f\'\'(x) = { (x-1)^2 * (2x-2) - (x^2-2x) * (2(x-1))} / (x-1)^4 ={2 * (x-1)^3 - 2 x(x-2) (x-1)} /(x-1)^4 f\'\'(0)<0 => local maxima => f(0)= 0 f\'\'(2)>0 => local minima f(2)= 4/1=4
