Calculus 1
posted by TayB .
Use Newton's method to find the coordinates, correct to six decimal places, of the point on the parabola y = (x − 5)^2 that is closest to the origin.

Calculus 1 
Nardos
Two cars A and B are moving along a straight road in the same direction withe velocity of 25km/h and 40km/h, respectively. Find the velocity of car B relatively to car A?

Calculus 1 
TayB
Nardos, did you post to the wrong question by accident. Because what you posted does not even relate to my question

TayB's question  Calculus 1 
Reiny
let the point of contact be (a,b), then
b = (a5)^2 = a^2  10a + 25
sketch the tangent and the normal
y' = 2(x5) = 2x  10
so the slope of the tangent at (a,b)
= 2a  10
and the slope of the NORMAL at (a,b)
= 1/(2a  10) or 1/(102a)
but using the old grade 9 way of doing slope ...
slope of normal = (b0)/(a0) = b/a
thus:
1/(102a) = b/a
a = 10b  2ab
subbing in b
a = 10(a^2  10a + 25)  2a(a^2  10a + 25)
a = 10a^2 100a + 250  2a^3 + 20a^2  50a
2a^3  30a^2 + 151a  250 = 0
using x instead of a,
f(x) = 2x^3  30x^2 + 151x  250
f ' (x) = 6x^2  60x + 151
by Newtons' Method, the simplified expression is
newx = (4x^3  30x^2 + 250)/(6x^2  60x + 151)
according to my sketch x = 3.5 might be a good starting point
newx = 3.765227...
next newx = 3.765227..
I think we got it after two iterations
carry on, you have the x, now find the y 
Calculus 1 
Anonymous
Reiny,
Aren't we supposed to use distance formula for this though?
Respond to this Question
Similar Questions

Calculus
Of the infinitely many lines that are tangent to the curve y = −7 sin x and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places. 
Calc 1
Of the infinitely many lines that are tangent to the curve y = −6 sin x and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places. 
Calc 1
Use Newton's method to find the coordinates, correct to six decimal places, of the point on the parabola y =(x − 5)^2 that is closest to the origin. 
Calc 1
Use Newton's method to find the coordinates, correct to six decimal places, of the point on the parabola y =(x − 5)^2 that is closest to the origin. 
Calc 1
Of the infinitely many lines that are tangent to the curve y = −6 sin x and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places. 
Calculus 1
Use Newton's method to find all roots of the equation correct to six decimal places. (Enter your answers as a commaseparated list.) (x − 9)^2 =ln x 
Calculus 1
Of the infinitely many lines that are tangent to the curve y = −4 sin x and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places. 
Calculus 1
Of the infinitely many lines that are tangent to the curve y = −4 sin x and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places. 
Calculus 1
Use Newton's method to find the coordinates, correct to six decimal places, of the point on the parabola y = (x − 5)^2 that is closest to the origin. 
Calculus 1
Use Newton's method to approximate the indicated root of the equation correct to six decimal places. The root of x^4 − 2x^3 + 5x^2 − 5 = 0 in the interval [1, 2]