Asked by Fizza Nadeem

Find the intervals in which the graph of tan inverse 1is concave upward and concave downward

Answers

Answered by oobleck
Just from looking at the graph, I'd say
upward: (∞,0)
downward: (0,∞)
But let's check f"(x) to be sure
f(x) = arctan(x)
f'(x) = 1/(x^2+1)
f"(x) = -2x/(x^2+1)^2
So we see that I was right at first.
f"(x) > 0 on (-∞,0)
f"(x) < 0 on (0,∞)
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