Find the minimum value of f(x)=(x^2+1/x)/(x^2-(1-1/x^2)/(1/x+1/x^2) over the interval 1lexle2. Write your answer as an exact decimal?
1 Answer
Dec 17, 2017
Explanation:
f(x) = (x^2+1/x)/(x^2-(1-1/x^2)/(1/x+1/x^2))
color(white)(f(x)) = (x^2+1/x)/(x^2-(x^2-1)/(x+1)
color(white)(f(x)) = (x^2+1/x)/(x^2-(x-1))
color(white)(f(x)) = (x^2+1/x)/(x^2-x+1)
color(white)(f(x)) = (x^3+1)/(x(x^2-x+1))
color(white)(f(x)) = ((x+1)(x^2-x+1))/(x(x^2-x+1))
color(white)(f(x)) = (x+1)/x
color(white)(f(x)) = 1+1/x
This function is monotonically decreasing over the interval
So the minimum value occurs when