Monday

September 15, 2014

September 15, 2014

Posted by **kyle** on Sunday, January 16, 2011 at 10:47pm.

My book says you use the distance formula.

Then you let L = D^2 because the minimum value of D^2 will occur at the same value of x as the minimum value of D.

What is L, though.

- calculus -
**bobpursley**, Sunday, January 16, 2011 at 11:06pmL is the distance^2. You dont have to do that way, as I will demonstrate.

D^2=(4- x)^2+(0-y)^2 that comes from the distance formula.

Doing it the way the L=D^2 did:

L= ..

dL/dx=0=2(4-x)+2(y)dy/dx

but dy/dx = d(sqrt x)/dx= 1/2sqrtx

so 0=-2x+2sqrtx/2sqrtx or

2x=2

x= 1/2, y= 1/sqrt2

Now, lets do it without the L substitution:

D^2=(4- x)^2+(0-y)^2 that comes from the distance formula.

2D dD/dx=0=2(4-x)+2(y)dy/dx

again, dy/dx= d(sqrtx)/dx= 1/(2sqrtx)

so 0=-2x+2sqrtx/2sqrtx

and again x=1/2, y= 1/sqrt2

- calculus -
**Reiny**, Sunday, January 16, 2011 at 11:13pmThey are saying, let D^2 = L

so when later on you differentiate

the result for L is simpler than that for D^2

They are using the property that if a > b

then a^2 > b^2.

let the closest point be P(x,y)

then

L = D^2 = (x-4)^2 + (y-0)^2

= (x-4)^2 + (x^(1/2))^2

= (x-4)^2 + x

dL/dx = 2(x-4) + 1 = 0 for a min distance

2x - 8 + 1 = 0

x = 7/2

if x=7/2 , then y = √(7/2) = √7/√2 = √14/2

the closest point is ((7/2 , √14/2)

**Answer this Question**

**Related Questions**

calculus - Consider line segments which are tangent to a point on the right half...

Math (repost, URGENT) - A curve is traced by a point P(x,y) which moves such ...

Math - A curve is traced by a point P(x,y) which moves such that its distance ...

calculus - Consider line segments which are tangent to a point on the right half...

calculus - My teacher told me to use the distance formula for this problem but ...

AP Calculus - Consider the curve given by x^2+4y^2=7+3xy a) Show that dy/dx=(3y-...

calculus - Find the point on the function y= 1/ x, x>0 that is closest to ...

????Math Question????8th grade adv.math - Algebra! How is the distance formula ...

calculus - Consider the curve given by the equation y^3+3x^2y+13=0 a.find dy/dx...

Calculus - Find the point on the graph of y = x^2 + 1 that’s closest to the ...