Posted by **Daryl** on Saturday, December 15, 2012 at 9:28pm.

Given y=(x)^1/2, find the closest point to (3/2,0)

- Calc-optimization -
**Reiny**, Saturday, December 15, 2012 at 11:39pm
let the closest point be P(a,b)

label the given point A(3/2 , 0)

AP will have a minimum length when AP is perpendicular to the tangent at P

slope of tangent = y' = (1/2)x^(-1/2) or 1/(2√x)

so at P the slope of the tangent is 1/2√a

slope of AP = b/(a-3/2)

b/(a-3/2) = -2√a , (the negative reciprocal of 1/2√a

but also b = √a

√a/(a-3/2) = -2√a

1/(a-3/2) = -2

1 = -2a + 3

2a = 2

a = 1

then b=√1 = 1

the closest point is (1,1)

## Answer This Question

## Related Questions

- calculus - optimization find the point on the graph of the function that is ...
- Calculus I - section is on Optimization: Find the point on the curve y = x^2 ...
- Calculus - Find the point on the graph of y=2x-4 that is closest to the point (1...
- Calculus-Applied Optimization Problem: - Find the point on the line 6x + 3y-3 =...
- Optimization - Calculus - Find the point closest to the line sqroot(X+1) from ...
- a ton of calc - basically, my teacher gave us a bunch of optimization problems ...
- Calc - Find the point on the line –2x+2y–3=0 which is closest to the point (–4–4...
- Pre-Calc - I am seeking help with this problem Please...Thank you! Find the ...
- Calc - Find the point on the parabola x+y^2=0 that is closest to the point (0,-3...
- calc - Find the point on the line 2 x + 6 y + 2 = 0 which is closest to the ...

More Related Questions