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How to prove concave and convex must be linear function?

Question:

How to prove concave and convex must be linear function?

Concavity:

The concavity of a function can be concave or convex we easily identify the type of concavity with the graph and the second derivative of the function under study.

Answer and Explanation:

When we have a linear function, the function has no concavity, when we have a non-linear function, we can find the concavity of the function with the second derivative test, if the test result is positive the function is concave, instead, if the result is negative, the function is convex.


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Concavity and Inflection Points on Graphs

from Math 104: Calculus

Chapter 9 / Lesson 5
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