Consider the line y=1 x -1 and the point P=(2,0). (a) Write the formula for a function d(x) that describes the distance between

Question

Consider the line y=1 x -1 and the point P=(2,0).

(a) Write the formula for a function d(x) that describes the distance between the point P and a point (x,y) on the line. You final answer should only involve the variable x. Then d(x) =

(b) d'(x)=

(c) The critical number is x= .

(d) The closest point on the line to P is ( , ).

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Ximena 3 weeks 2021-09-24T15:55:22+00:00 1 Answer 0

Answers ( )

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    2021-09-24T15:56:54+00:00

    Answer:

    Step-by-step explanation:

    d(x)=√((x-2)2+(y-0)²)

    =√((x-2)²+y²)

    =√((x-2)²+(x-1)²)

    =√(x²-4x+4+x²-2x+1)

    =√(2x²-6x+5)

    D=d²(x)=2x²-6x+5

    b.\\\frac{dD}{dx}=4x-6\\\frac{dD}{dx}=0,gives \\4x-6=0\\x=\frac{3}{2}\\\frac{d^2D}{dx^2}=4 >0 at x=\frac{3}{2}\\so~D~or~d^2~or~d~is~minimum~at~x=\frac{3}{2}\\so~y=1(\frac{3}{2} )-1=1/2=0.5\\so~nearest~point~is~(1.5,0.5)

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