How to find critical points from first derivative graph?

The first derivative of the curve at a critical point is zero. To find the critical points of a particular equation, we can differentiate the function and then set the resulting value to zero. Here is a step-by-step guide to finding the critical points of a function.

How to find critical points from intersection of first derivative and second derivative?

If the first derivative of a function at any given point is zero, then the function is either locally increasing or decreasing at that point. A critical point is a point at which both the first derivative and the second derivative are zero. These are points at which the function either has a maximum or a minimum. If the first derivative is zero, then the second derivative is not defined. To find critical points, you need to graph the first derivative and the second derivative. Intersection of graphs of first derivative

How to find critical points from intersection of first derivative and x axis?

Intersection of the first derivative and x axis is a quick way to get an idea of where the function is increasing or decreasing fastest. Some points may be minima, others might be maxima, and still others might be stationary or have no first derivative at all. If we can locate these points, we can use them to determine the critical points. As you can see in the example graph below, the function is decreasing fastest at the point where the line crosses the x axis again. This means

How to find critical points from intersection of first derivative and y axis?

If you are dealing with a function with an absolute maximum or minimum, then the first derivative of that function will be 0 at the critical point. If the function has no absolute maximum or minimum, then the first derivative will be zero at a critical point if it goes through the origin. If the first derivative has no zeros, then you cannot determine if there is a critical point or not.

How to find critical points from $

When we have a graph of a function $f$, it is easy to find its critical points. Take the first derivative of $f$, find the zeros of the function and name the critical points. However, it is not that easy for more sophisticated graphs. If your graph is in the form of a Cartesian graph, it is still possible to locate the minima, maxima and saddle points. However, if your graph is in a polar form, the location of the critical points becomes