Question

. For the function f(x) = x 1+x2

(a) find the intervals on which the function is increasing or decreasing

(b) determine the points of local maximum and local minimum

(c) find the asymptotes.

Answer 1

Differentiating with respect to x

(Because )

For critical points

(a)

Function is increasing if

Function is decreasing if

(b)

at x=-1

(Local minimum if f'(x)=0 and if sign of f'(x) is changing from negative to positive)

at x=1

(Local maximum if f'(x)=0 and if sign of f'(x) is changing from positive to negative)

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(c)

Asymptotes

Vertical asymtotes: None

Horizonatal asymptotes