2.6 Question 3

[Eigenvalue]

Precalculus
Michael Sullivan
Edition 4
Chapter 2, Section 2.6

Let P=(x,y) be a point on the graph of y=[tex]\sqrt{x}[/tex]

a) express the distance d front P to point (1,0) as a function of x

b) Use a graphing utility to graph d=d(x)

c) For what values of x is d the smallest?

[nycmath]

Part A


Use d = [tex]\sqrt{(x-1)^2+(y-0)^2}[/tex]

d = [tex]\sqrt{(x-1)(x-1)+y^2}[/tex]

d = [tex]\sqrt{x^2-2x+1 + ( \sqrt{x} })^2[/tex]

d = [tex]\sqrt{x^2-2x+1 + x}[/tex]

d = [tex]\sqrt{x^2-x+1}[/tex]

We want d(x).

d(x) = [tex]\sqrt{x^2-x+1}[/tex]

[nycmath]

Part B

This is the graph of d(x) = [tex]\sqrt{x^2-x+1}[/tex]

[nycmath]

Part C

Based on the graph in Part B, the distance d is the smallest when x = 0.5.

You say?