Constant : Constant is another word for a fixed number that is mainly used in the context of expressions or functions like $f(x)=c$ that are equal to the same number irrespective of any variable.

Derivative : A derivative of $f$ also written as $f^{\prime}$ or $\frac{d}{dx}f$ or $\frac{df}{dx}$ is defined by $f^{\prime}(x)=\lim \limits_{h\to 0}\frac{f(x+h)-f(x)}{h}.$ The derivative $f^{\prime}(x)$ can be interpreted as the speed at which the function value is changing or as the slope of the tangent in the graph of $f$ at $x$. For example the derivative of a constant function is 0, the derivative of $f(x)=x$ is 1 and the derivative of $x^2$ is $2x.$ All local extrema of differentiable functions $f$ are roots of the derivative of $f.$

Function : A function is a mapping in which every element in one set is mapped to exactly one element of a second set. Most often the mapping is described using a rule. For example the function $f(x)=x+1$ maps 2 to 3 and -1 to 0.

Minimum : The minimum of a set of numbers is the lowest of the numbers in the set. A function has a minimum at $x_0$ if $f(x_0)\leq f(x)$ for all $x.$

Polynomial : A polynomial is an expression of the form $a_0+a_1x+a_2x^2+\ldots+a_nx^n$