Concave Function

Introduction to Concave Function

In this blog post, we will learn about the concave function present in Matlab. It is one of the most important functions in Matlab that is quite useful among programmers. Now the question arises of how one can find out whether the method is concave or convex. To find out this one need to look at the second derivative to determine whether it is concave or convex. Positive results have a convex shape. It is concave if the answer is negative.

Now in a more mathematical way, one can define the above difference as:

f(x) <= g(x) with f convex, and g concave

Here f denotes concave and -f denotes convex function respectively. Another way of representing the same is:

f(x)-g(x) <= 0 f-g is convex

Concave refers to geometric forms with an inward curvature, such as an hourglass. Shapes that curve outward, like a football, are convex. Apart from this method, one should also know about the graph of the concave function. If the tangent line to the graph at that point is above the graph in the area surrounding the point, the graph is said to be concave down at that point, and vice versa. The above blog post will surely give you an idea about this important method in Matlab. 

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