Global Maxima and Minima of a function? When we put the derivative of the a function = 0 and solve for it then what do we get ? Local Maxima or Minima or Global extrema or Global minima ?
 A: 
If $f$ is differentiable and continuous on the interval $[a,b]$, then global maximum of $f$ in the interval $[a,b]$ exists and is one of the points $a,b$ or a point $c\in(a,b)$ such that $f'(c)=0$.

A same theorem also holds for total minimum, hence for finding global maxima (minima) we just find the maximum (minimum) value(s) of $f$ at the points $\{a,b\}\cup\{c\in(a,b)|f'(c)=0\}$.
Observe that in every local maximum or minimum $c\in(a,b)$ of $f$ we have $f'(c)=0$, but if for some $c\in(a,b)$ $f'(c)=0$ we can't deduce that $c$ is a local maximum or local minimum. For an example look at the function $f(x)=x^3$ at $c=0$.
A: When $x=0$ it is only local maxima,minima or point of inflection 
The local maxima or minima can be the global maxima or minima. That has to be obtained be one more test ie: To look at the function's value at $±\infty$ and also when $x\to a^{±}$ where function is discontinuous at a.
After obtaining this much data you get global maxima or minima.
In the illustration:
The black line is a cubic polynomial. It has a local maxima and minima but as we go to $±\infty$ we get the global maxima/minima.
The red line is a quadratic polynomial, we have a local minima which is also the global minima. $±\infty$ gives us global maxima.
The green line is the reciprocal function $\left(\frac{x}{1-x}\right)$ as you can see as $x\to 1^+$ we have global maxima but $x\to 1^- $ it is global minima.

