Sunday

November 23, 2014

November 23, 2014

Posted by **Mishaka** on Friday, December 16, 2011 at 9:51pm.

- Calculus -
**drwls**, Saturday, December 17, 2011 at 5:30amDistance to point, squared, is:

R^2 = (x-8)^2 + (y-1.5)^2

= (x-8)^2 + (x^2 -0.5)^2

Solve for the x value when d(R^2)/dx = 0

d/dx [x^2 -16x +64 + x^4 -x^2 + 1/4] = 0

2x -16 +3x^3 -2x = 0

3x^3 = 16

x = 1.747

y = 4.053

- Calculus - typo -
**Steve**, Saturday, December 17, 2011 at 6:35amNote that d/dx x^4 = 4x^3 not 3x^3

From there on, we have

2x - 16 + 4x^3 - 2x = 0

4x^3 = 16

x = cbrt(4)

y = cbrt(16)+1

Or, looking at things in another way, the normal line from point (p,q) on the curve will have the shortest distance to (8,1.5)

At any point (p,q) on the curve, the slope is 2p, so the normal line has slope -1/2p

Now we have a point and a slope:

(y-q)/(x-p) = -1/2p

y - p^2 - 1 = (p-x)/2p

1.5 = (p-8)/2p + p^2 + 1

3p = p - 8 + 2p^3 + 2p

2p^3 = 8

p^3 = 4

p = cbrt(4)

q = cbrt(16)+1

- Thanks -
**drwls**, Saturday, December 17, 2011 at 8:35amThanks Steve for noticing my error

**Answer this Question**

**Related Questions**

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

calculus - Find the point on the graph of f(x)=√x that is closest to the ...

calculus - optimization find the point on the graph of the function that is ...

Calculus - Find the point P on the graph of the function y=\sqrt{x} closest to ...

Calculus - find the point on the graph of the function that is closest to the ...

Calculus - Find the point on the graph of y=2x-4 that is closest to the point (1...

Calculus - Find the point on the graph of function that is closest to the point...

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

calculus - let f be the function f(x) = x^3 + 3x^2 - x + 2 a. the tangent to the...

Geometry - quadrilateral A B C D on a graph. Point A is at ( -5, -1), Point B ...