True or False: The graph of f(x) = 1 / x is concave downward for x less than 0 and concave upward for x greater than 0; therefore, there is a point of inflection at x = 0.
I said false because the graph is discontinuous at x = 0. Is my answer AND my reasoning correct?
Also, is what was stated about the concavity still true? I drew the graph and believe that their concavity statement is true. Am I correct?
2007-04-08 05:39:35 · 4 answers · asked by :-) 3 in Science & Mathematics ➔ Mathematics
You are bang on. Good job.
2007-04-08 05:43:19 · answer #1 · answered by Astronomer1980 3 · 1⤊ 0⤋
You are right. Being concave downward to the left of 0 and concave upward to the right does not say that x = 0 is a point of inflection, because that point does not exist. I don't know the exact reason, but surely a point must exist to be an inflection point.
They are right, though about the concavity. The second derivative, which gives the concavity, is f''(x) = 2 x^-3, so all negative numbers would give a negative value here for f''(x).
2007-04-08 05:59:41 · answer #2 · answered by David S 4 · 1⤊ 0⤋
False
2007-04-08 05:43:05 · answer #3 · answered by Melissa 2 · 1⤊ 0⤋
Yes you are correct
2007-04-08 07:22:08 · answer #4 · answered by santmann2002 7 · 0⤊ 0⤋