1. f(x) = x/x^2 + 1
2. e^2x + e^-x

a) Find the intervals on which f is increasing or decreasing
b) find local max and min
c) find intervals of concavity and inflection points

Thank You!

Question

1. f(x) = x/x^2 + 1 
2. e^2x + e^-x

a) Find the intervals on which f is increasing or decreasing
b) find local max and min
c) find intervals of concavity and inflection points

Thank You!

anonymous · Answer

$$f(x)=\frac{x}{x^2+1}$$
$$f'(x)=\frac{1-x^2}{(x^2+1)^2}$$
denominator is always positive, so this is positive if the numerator is

anonymous · Answer

solve $1-x^2>0$ since this is a parabola that faces down, it is positive between the zeros, namely on the interval $(-1,1)$ and negative otherwise

anonymous · Answer

therefore function is decreasing on $(-\infty,-1)\cup (1,\infty)$ and increasing on $(-1,1)$ as you can clearly see from the picture here http://www.wolframalpha.com/input/?i=x%2F%28x^2%2B1%29