Is this Cost function concave or convex? Given the following cost function, where t is the quantity of some product.

$$C(t) = 1/3t^3 - 7t^2 +11t + 50$$

here is a graph between $t= 0$ and $t = 25$



We are asked if this function is convex or concave?

Technically it is neither, but I am asking, in the context of economics, do we have to define intervals and say, between $0$ and $4.11$, it is concave, and for $t&gt;4.12$ we have a convex function?
"In the context of economics", it is neither - because convexity in economics means the same it does in math. If you redefine its domain, such that it's only computed for any $t &gt; 4.12$, this function's image is clearly convex: no line between two vectors inside it isn't entirely contained in the set.

P.S: Although convexity has the same definition in both fields, it has an important economic interpretation and is a very important hypothesis in many classical general equilibrium models.