How do you find all local maximum and minimum points given #y=x^2-x#?

1 Answer
Feb 3, 2018

Answer:

See explanation.

Explanation:

To find the local extreme (maximum or mininmum) of a function #f(x)# we have to find its derivative and check where it is zero.

Here we have:

#f(x)=x^2-x#

#f'(x)=2x-1#

#2x-1=0 iff x=1/2#

The point #x_0=1/2# can be a critical point of #f(x)#. To check if it is a critical point we have to find out if the derivative changes sign at #x_0=1/2#

graph{2x-1 [-2.738, 2.737, -1.37, 1.367]}

As we can see the derivative changes sign from negative to positive, so the point #x_0=1/2# is a minimum.

Answer:

The function #f(x)=x^2-x# has a minimum at #x_0=1/2#.