Calculus

Hey there. I have a quick question. Ive done questions like these before so I don't know whats stoping me. Anways the question is this:
Find a point on the graph of
y = x^2


with x>0 that lies closest to (0, 3). What is the x-coordinate of such a point?

So I got 3^2 + y^2 = x^2 and solved for x but after that I'm lost. Normally that's what we did, but our other equations was normally like xy=8 so now I'm kinda lost. Any help would be apperciated. Thanks

The distance d from apoint with coordinates (x,y) to the point (0,3) is given by:

d^2 = x^2 + (y-3)^2

You have to minimize this while satisfying the constraint that he point (x,y) be on te parabola. So the contraint is:

y = x^2

This means that:

d^2 = y + (y-3)^2

You have to minimize this function.



Okay, so would you mind checking this? I've lost so many points already I don't wanna enter any more wrong answers.
If we have d^2 = y + (y-3)^2 then d =(y + (y-3)^2) ^1/2 (aka the root is what im getting at) So then if I take the derivative and then make it equal zero I get y = 3, so then x would equal the root of 3?

Hmm well I guess I went wrong somwheres because I put that it and it says its not right.

Sorry again. I missed something when I did the derivative and while adding something together I forgot something out. So now I have that y=5/2 and x=sqrt5/2

This is correct. Note that you can just differentiate d^2 instead of d. The square of a positive function is minimal (maximal) if and only if the function itself is minimal (maximal).

  1. 👍 0
  2. 👎 0
  3. 👁 167
asked by Tracy

Respond to this Question

First Name

Your Response

Similar Questions

  1. very complicated maths

    Hey guys, need some help with a question ive been stuck on for a looooooong time! The question is: Given that (x+4) is a factor of the expression 3x^3+x^2+px+24, find the constant value of p. Hence factorise and solve the equation

    asked by Nikki Clark on November 21, 2012
  2. calculus

    hey guys, quick question (-8 +- sqrt -20)/-6 what does this equal

    asked by Karlie on September 11, 2015
  3. reading

    I need help with questions for the book a boy named slow.Thanks. The questions are 1.what happens when Returns again goes hunting 2.What big thing does slow do, 3.what else does he do to prepare himself for adulthood, 4.What does

    asked by ray on April 12, 2007
  4. Reading Analogy

    Hey Everyone! I have a quick question! I'm doing this reading packet and you have to find out the relationship between the two words... Insect:termite would that be classification? or something else?

    asked by Hello! on April 14, 2009
  5. Geo

    Just a quick question that will help me in my essay. I just need a quick answer not an explination, Im just using this answer as a quick refernce. Question: What is the most common precipitation in New Brunswick. I just need a

    asked by London on January 14, 2007
  6. Factoring Trinomials

    Working on how to factor trinomials, and the method that works best for me is the criss cross method, so Ive sticked with it. But Ive been stuck on one question for the past few minutes, and don't know what I've been doing wrong.

    asked by -Untamed- on October 31, 2011
  7. chemistry

    Predict the precipitate that forms: HCl + AgNO3 --> ??? i don't know what the answer is but i think it is Cing04 AgCl. You need to learn the solubility rules. If you don't have a web site I can give you one. hey watz up can you

    asked by key on January 29, 2007
  8. Algebra

    Hey, hot question real quick. I am doing Functions in Algebra and I kinda need help. So the function I have is **g(x)=x^2-9** and I have to evaluate **g^-1(x)**, but my question is how does the exponent go in front of the numbers?

    asked by . on February 5, 2019
  9. math-moneyfractions

    i have some math questions that i really ,really,need help with asap if any body can explain some of these questions that will be great help.Ok here are 3 of the questions i am about to type now ok the first one says,whole 16

    asked by chemaya on February 18, 2009
  10. Java Programming

    Hi, Could any please have look at the question and my work below? Thanks! www.jiskha(dot)com/questions/1803696/Hi-Im-new-to-Java-Ive-been-working-on-this-question-wrote-the-code-and-checked

    asked by Ashley on October 4, 2019

More Similar Questions