How do you plot a function on a cartesian plane?
There is a procedure to graph a function.
Define the domain and codomain
Find the intersection between function and x-axes:
Calculate the first derivative and its intersection with x-axes:
#f'(x)=0#. This points are called extrema, geometrically represent the points where the tangent of the function is horizontal. This mean that the function reach its minimum or maximum or stationary points.
Calculate the second derivative and its intersection with x-axes:
#f''(x)=0#. This points (inflection point) are points on a curve at which the curve changes from being concave to convex or vice versa.
#f''(x)>0 #the function is convex (is smiling)
#f''(x)<0 #the function is concave (is sad)