Hey all, could someone please check my answers? thanks

1.) Consider the function k(x) = (x^2+1)arctan(x)

Useful Information:

k'(x) = 1+2xarctan(x)

k''(x) = (2x/x^2+1)+ 2arctan(x)

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a) Find the domain of k

my solution: dom(k) = R

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b) Find x and y intercepts

my solution x int at (0,0) and y int at (0,0)

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c) Find the interval on which k is increasing:

my solution: since k'(x) > 0 on (0,inf), k increases from (0,inf)

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d) Find the interval on which k is decreasing

my solution: since k'(x) < 0 on (-inf,0), k decreases from (-inf, 0)

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e) Does k have any stationary points?

my solution: k'(x) = 0

1+2xarctan(x) = 0

arctan(x) = -(1/2x)

since the two graphs never intersect, there are no stationary points

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f) show that k has point of inflection at x = 0

my solution: k''(0) = 0, therefore point of inflection.

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g) Is the point of inflection at x = 0 stationary or non stationary?

my solution: k'(0) = 1, therefore non stationary point of inflection at x = 0

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h) Does k have any other point of inflections?

my solution: k''(x) = 0

(2x/1+x^2)+2 arctan(x) = 0

I got stuck at this point, any guidance would be much appreciated.

Thanks.