How do you find the stationary points of a function?

Question

23904 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-26T12:05:31

Shown below

enter image source here

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 ) #