fx = 0 when x = -3 or x = 1simba_ said:Homework Statement
Find the critical points of
x3 + y3 + 3x2 + 6y2 - 9x + 9y +1
you do not need to define the critical points
Homework Equations
The Attempt at a Solution
i have
df/dx = 3x2 + 6x - 9 and when i solve this x = -3, 1
but i don't know what the corresponding y values are
df dy = 3y2 + 12y + 9 and so y = -3, -1
and here i don't know what the corresponding x values are
Critical points are points on a graph or function where the derivative or gradient is equal to zero. They are also known as stationary points.
To find the critical points of a function, you need to take the derivative of the function and set it equal to zero. Then, solve for the variable to find the critical points.
Critical points are important because they can tell us about the behavior of a function. They can indicate the maximum, minimum, or inflection points of a function.
A local critical point is a point on a function where the derivative is equal to zero and it is either a maximum or a minimum within a specific interval. A global critical point is a point on a function where the derivative is equal to zero and it is the maximum or minimum value for the entire function.
Yes, a function can have multiple critical points. These points can be local or global and they can occur at different locations on the function's graph.