You will need
- - the function you want to examine for the presence of stationary points;
- - definition of stationary points: a stationary point of a function is the point (value) where the derivative of the first order vanishes.
Instruction
1
Using a table of derivatives and differentiation formula of the functions, it is necessary to find the derivative of the function. This step is the most difficult and responsible in performing tasks. If you make a mistake at this stage, further calculations will have no meaning.
2
Check whether derivative of the function from the argument. If you find the derivative does not depend on the argument, then there is a number (for example, f'(x) = 5), in this case, the function has no stationary points. Such a solution is possible only if the investigated function is a linear function of the first order (for example, f(x) = 5x+1). If the derivative of a function depends on the argument, then proceed to the last step.
3
Write down the equation f'(x)= 0 and solve it. The equation may not have solutions - in this case, the function's stationary points is not available. If the solution to the equation is that these are the values of the argument and will be stationary points of the function. At this stage you should inspect the solution of equation method substitution argument.
Note
When finding the derivative of the function can be difficult if the function is complex. In this case you need to use the replace function part, the intermediate argument.
Useful advice
To perform this task, you must pay special attention to the rules of differentiation.
Attention and concentration on the task will also help to deal with it - before running, make sure that you don't get distracted in the decision process.
Knowledge of the stationary points of a function greatly facilitates the construction of its graph, as it is at these points is the maximum and minimum values of the function.
Attention and concentration on the task will also help to deal with it - before running, make sure that you don't get distracted in the decision process.
Knowledge of the stationary points of a function greatly facilitates the construction of its graph, as it is at these points is the maximum and minimum values of the function.
