Question

Find the critical points, and the points of inflection y= (x+1)^2/x

Help me please!!!

Answer 1

Did you use the quotient rule?

y' = (x(2)(x+1) - (x+1)^2)/x^2
= (2x^2 + 2x - x^2 - 2x -1)/x^2
= (x^2 - 1)/x^2

set this equal to zero

(x^2 - 1)/x^2 = 0
x^2 - 1 = 0
x^2 = 1
x = ± 1

if x = 1, y = 4
if x = -1 , y = 0

check:
http://www.wolframalpha.com/input/?i=y%3D+(x%2B1)%5E2%2Fx

for point of inflection, find y'' using the quotient again.
According to Wolfram's diagram , there should be no point of inflection.
Make sure your algebra shows that.