What are the critical points of f(x) = sqrt((x^2 - 4x +5))f(x)=(x24x+5)?

1 Answer
Apr 16, 2018

The critical point off(x)f(x) is (2,1)(2,1)

Explanation:

y=sqrt(x^2-4x+5)y=x24x+5

Differentiate

y'=(2x-4)/(2sqrt(x^2-4x+5))

now critical points are points at which y'=0 or the tangent is vertical at that point i.e. y'=1/0

y'=0color(blue)rarr2x-4=0

x=2

y'=1/0color(blue)rarrx^2-4x+5=0

x=2+-i which it refused as it's not a real number

So there is one critical point at x=2
f(2)=1

The critical point off(x) is (2,1)