find all points where y'=0

Question

For each function below, find all points where y'= 0.
(a) y =√(x² − x)
(b) y = xe^-x

Answer 1

We take derivative of each function and set it equal to zero..  This also allows us to find the critical point on the graph which can be used to determine the minimum and maximum points.

 

Part a)

 

[(x² - x)^1/2]' = 0

 

(1/2)(x² - x)^-1/2(2x - 1) = 0

 

(x - (1/2)) / √(x² - x) = 0

 

The critical point is x = 1/2

 

 

Part b)

 

(xe^-x)' = 0

 

e^-x - xe^-x = 0

 

e^-x (1 - x) = 0

 

The critical point is x = 1