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,∞)
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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