Any graph should be titled and have maximum and minimum values listed on it. The minimum values are usually on the bottom left and the maximum values are on the top right and bottom right of the graph.
Apex.
When you look at the parabola if it opens downwards then the parabola has a maximum value (because it is the highest point on the graph) if it opens upward then the parabola has a minimum value (because it's the lowest possible point on the graph)
Both the function "cos x" and the function "sin x" have a maximum value of 1, and a minimum value of -1.
It is a graph in three dimensions, relative to the x-, y- and z-axes.
the maximum, turning point, peak ?
No, since the equation could be y = x3 (or something similar) which will have a point of inflection at (0,0), meaning there is no relative maximum/minimum, as the graph doesn't double back on itself For those that are unfamiliar with a point of inflection <http://mathsfirst.massey.ac.nz/Calculus/SignsOfDer/images/Introduction/POIinc.png>
Apex.
When you look at the parabola if it opens downwards then the parabola has a maximum value (because it is the highest point on the graph) if it opens upward then the parabola has a minimum value (because it's the lowest possible point on the graph)
It has an absolute minimum at the point (2,3). It has no maximum but the ends of the graph both approach infinity.
vertex
Both the function "cos x" and the function "sin x" have a maximum value of 1, and a minimum value of -1.
Assuming the standard x and y axes, the range is the maximum value of y minus minimum value of y; and the domain is the maximum value of x minus minimum value of x.
A quadratic can be drawn as a graph and it is either "U" shaped or "n" shaped. If it were "U" shaped, the minimum value qould be the lowest point of the "U". If "n" shaped, maximum would be the top.
If x2 is negative it will have a maximum value If x2 is positive it will have a minimum value
For a general cosine graph, they would be the maximum and minimum values, and the values of the independent variable at which these are attained.Note that the graph of y = cos(x)+2 is never equal to zero, so there may not be any roots.
If the arrows of the graph point down, then the vertex is a maximum because it is the greatest point on the graph. If the arrows point up, then the vertex is the minimum because it is the lowest point.
This means that the function has reached a local maximum or minimum. Since the graph of the derivative crosses the x-axis, then this means the derivative is zero at the point of intersection. When a derivative is equal to zero then the function has reached a "flat" spot for that instant. If the graph of the derivative crosses from positive x to negative x, then this indicates a local maximum. Likewise, if the graph of the derivative crosses from negative x to positive x then this indicates a local minimum.