How do you find the stationary points of a function?

Question

Charles Arocha · Accepted Answer

Shown below

As we can see from this image, a stationary point is a point on a curve where the slop is zero

Hence the stationary points are when the derivative is zero

Hence to find the stationary point of #y = f(x) #, find #(dy)/(dx) # and then set it equal to zero

#=> (dy)/(dx) = 0 #

Then solve this equation, to find the values of #x # for what the function is stationary

For examples

#y= x^2 + 3x +8 #

To find the stationary find #(dy)/(dx) #

# (dy)/(dx) = 2x + 3 #

Set it to zero

#2x+3 = 0 #

Solve

#x = -3/2 => y= 23/4 #

Hence the stationary point of this function is at #(-3/2 , 23/4 ) #

Christopher Allers · Answer

undefined To find the stationary points of a function, follow these steps:

1. Compute the first derivative of the function.
2. Set the first derivative equal to zero and solve for the variable(s). These values are potential stationary points.
3. Check the second derivative of the function at each potential stationary point.
4. If the second derivative is positive, the point is a local minimum; if negative, it's a local maximum; if zero, further tests are needed (such as the first derivative test or higher-order derivatives) to determine the nature of the stationary point.
5. Repeat the process for any additional variables if the function is multivariable.