How do you find the critical points of a rational function?
To find the critical points of a function, first ensure that the function is differentiable, and then take the derivative. Next, find all values of the function's independent variable for which the derivative is equal to 0, along with those for which the derivative does not exist. These are our critical points.
The critical points of a function
A) The function exists.
B) The derivative of the function
As an example with a polynomial function, suppose I take the function
For our first type of critical point, those where the derivative is equal to zero, I simply set the derivative equal to 0. Doing this, I find that the only point where the derivative is 0 is at
For our second type of critical point, I look to see if there are any values of
For a slightly more tricky example, we will take the function