phillyolly said:Homework Statement
g(y)=(y-1)/(y2-y+1)
Homework Equations
The Attempt at a Solution
After I take a derivative, I get
g'(y)=[y(y-2)]/(y2-y+1)2
However,
(y2-y+1)2 does not have any solutions. Am I right that I just throw it away? As an answer, I only leave
y1=0, y2=2
Is that correct?
The critical numbers of a function help us determine where the function's maximum and minimum values occur. They are also used to help us find the function's inflection points.
To find the critical numbers of a function, we need to find the points where the derivative of the function is equal to zero or undefined. This can be done by setting the derivative equal to zero and solving for the variable, or by finding the points where the derivative is undefined.
Critical numbers are important in calculus because they help us analyze the behavior of a function. They tell us where the function has extreme values and where it changes from increasing to decreasing or vice versa. This information is crucial in understanding the overall shape and behavior of a function.
Yes, a function can have more than one critical number. In fact, most functions have multiple critical numbers, unless they are constant or have a very simple shape. This is because a function can have multiple points where the derivative is equal to zero or undefined.
A critical number is a point on a function where the derivative is equal to zero or undefined. It indicates a change in the slope of the function. An inflection point, on the other hand, is a point where the concavity of the function changes. It is determined by the second derivative of the function and does not necessarily correspond to a critical number.