|Find the interval on which the curve of | | ...


Find the interval on which the curve of
is concave up


For a curve represented by a function, concavity refers to the change in curvature of the graph from the curvature being concave upwards to concave downwards or vice-versa. The curvature is concave upwards in the interval where the second derivative of that function is positive.

Answer and Explanation:

Let {eq}f(x)=x^2+4 {/eq}

{eq}\Rightarrow f'(x)=2x\\\Rightarrow f''(x)=2>0 {/eq}

Hence, the above function is concave upward everywhere on the set of real numbers i.e., {eq}(-\infty,\infty) {/eq}

Learn more about this topic:

Concavity and Inflection Points on Graphs

from Math 104: Calculus

Chapter 9 / Lesson 5

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