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Problem 64 Hard Difficulty

Estimate the intervals of concavity to one decimal place by using a computer algebra system to compute and graph $ f" $.

$ f(x) = \frac{x^2 \tan^{-1} x+}{1 + x^3} $

Answer

Graph of $f(x)$ is concave up in the interval $(-\infty,-1) \cup(0,0.7) \cup(2.5, \infty)$
Graph of $f(x)$ is concave down in the interval $(-1,0) \cup(0.7,2.5)$

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Video Transcript

okay. Using a computer program to Graff. Thus, we know over here that the graph intersects the Y axis three places X equals zero X equals 0.7 and X equals 2.5. We know the graphics can give up from negative infinity. Tonight you have 10 to 0.7 and 2.5 to infinity and conclave, down from negative 1 to 0 and 0.7 to 2.5.