What does your textbook say about finding critical points?n.a.s.h said:Homework Statement
find the derivative and critical points of the function
f(x)= x^3-x^2+5
Homework Equations
The Attempt at a Solution
I tried to find the derivative: 3x^2-2x but I am not sure how to find the critical points from here...
A critical point of a function is a point where the derivative of the function is equal to 0 or undefined. It can also be described as a point where the slope of the function is changing from positive to negative or vice versa.
To find critical points of a function, you must first take the derivative of the function. Then, set the derivative equal to 0 and solve for the variable. The solutions to this equation will be the critical points of the function. You can also use the second derivative test to confirm if a critical point is a maximum, minimum, or inflection point.
Critical points are important in understanding the behavior of a function. They can indicate where the function has a maximum or minimum value, as well as where the function changes direction. This information can be useful in optimization problems and in graphing a function.
Yes, a function can have multiple critical points. This can occur when the function has multiple local extrema or inflection points. It is also possible for a function to have no critical points.
A critical point is a point where the derivative of a function is equal to 0 or undefined, while a singular point is a point where the function itself is undefined. Singular points can occur at critical points, but they can also occur at other points where the function is not continuous or differentiable.