Question

Find the points on the graph of (x+6)^2 that are closest to the point (-3,0)

Answer 1

a point on the graph is \((x, (x+6)^2)\) and the square of the distance will be
\[(x+3)^2+(x+6)^4\]
minimize that one

Answer 2

do i have to factor all that out?

Answer 3

i hope this is a calculus course
you have to take the derivative, set it equal to zero and solve to find the critical points

Answer 4

btw it is already factored, but if you like you could multiply it
might make it easier

Answer 5

yes it is calculus. multiplying to is going to take a long time but thanks! :)

Answer 6

takes a nano second
http://www.wolframalpha.com/input/?i=%28x%2B3%29^2%2B%28x%2B6%29^4

Answer 7

oh thank you so much! I remember using that website in the past but i forgot the name.
Also i have another question. Would you please help me on it:
A rectangular solid with a square base has a volume of 6859 cubic inches. (Let x represent the length of the sides of the square base and let y represent the height.)
(a) Determine the dimensions that yield the minimum surface area.

Answer 8

surface area is \(2x^2+4xy\)
and since volume is \(6859\) you know \(x^2y=6859\) making \(y=\frac{6859}{x^2}\) and the surface area is now
\[S(x)=2x^2+\frac{4\times 6859}{x^3}\]

Answer 9

ok that was wrong
surface area is ow
\[S(x)=2x^2+\frac{4\times 6859}{x}\]

Answer 10

so now you would take the derivative and set it equal to zero right?

Answer 11

yes

Answer 12

ok thanks! You are a life saver!!! :D

Answer 13

yw

Answer 14

ok for x I got 19 but how do you find the other side? do you plug it back into the original?

Answer 15

oh nevermind i got it