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# Estimate the intervals of concavity to one decimal place by using a computer algebra system to compute and graph $f"$.$f(x) = \frac{x^2 \tan^{-1} x+}{1 + x^3}$

## 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 $(-1,0) \cup(0.7,2.5)$

Derivatives

Differentiation

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

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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.

#### Topics

Derivatives

Differentiation

Volume

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

Lectures

Join Bootcamp