• May 20th 2006, 03:31 AM
diudiu
Well there is this function

E(x) = w sqrt[x^2 + 10000] + 50 sqrt[5] - x

Question: Suppose that w = 2 use ure graphics calculator to draw the graph of E(x) and find the x value for which E(x) is a minimum. Specify a suitable domain for x and explain why you have chosen this particular domain.

The domain i BELIEVE to be: 0 < x < 111.8

But i really don't understand the theory as to explaining WHY ..

• May 20th 2006, 05:24 AM
earboth
Quote:

Originally Posted by diudiu
Well there is this function

E(x) = w sqrt[x^2 + 10000] + 50 sqrt[5] - x

Question: Suppose that w = 2 use ure graphics calculator to draw the graph of E(x) and find the x value for which E(x) is a minimum. Specify a suitable domain for x and explain why you have chosen this particular domain.
The domain i BELIEVE to be: 0 < x < 111.8
But i really don't understand the theory as to explaining WHY ..

Hello,

$E(x)=2 \cdot \sqrt{x^2+10000}+50 \cdot \sqrt{5} - x$

I've attached a diagram of this function.

The domain is a subset of the real numbers which are allowed with your function. There are a few restrictions, which you have to consider:
1. Division by zero is forbidden.
2. Squareroot of a negative number is not a real number.
3. Logarithms of zero or negative numbers are not real.

Your fuction doesn't deal with all these restrictions . Thus the domain of your function is $\mathbb{R}$

What bothers me a little bit is: Why do you believe that the domain is $0

The derivative of your function is (Don't forget to use the chain rule!):

${dE_2 \over dx}=2 \cdot {1\over2} \cdot \left(x^2+10000 \right)^{-{1\over2}}\cdot 2x-1$ = ${2x\over\sqrt{x^2+10000}}-1$

You'll get an extreme value (maximum or minimum) of this function if the derivative equals zero:

${2x\over\sqrt{x^2+10000}}-1=0 \Longleftrightarrow {2x\over\sqrt{x^2+10000}}=1\ , x>0$

Multiply by the denominator and afterwards square both sides of the equation. You'll get:

$3x^2=10000 \Longleftrightarrow x_1 \approx -57.735\ \vee \ x_2 \approx 57.735$

E(57.735) = 285.0085

Greetings

EB
• May 20th 2006, 10:37 AM
topsquark
Quote:

Originally Posted by diudiu
Well there is this function

E(x) = w sqrt[x^2 + 10000] + 50 sqrt[5] - x

Question: Suppose that w = 2 use ure graphics calculator to draw the graph of E(x) and find the x value for which E(x) is a minimum. Specify a suitable domain for x and explain why you have chosen this particular domain.

The domain i BELIEVE to be: 0 < x < 111.8

But i really don't understand the theory as to explaining WHY ..

Earboth: I believe he's looking for what domain to put into his calculator viewing window.

Generally what you want for the domain is a large enough region of the x-axis to show all the "features" of a graph. There isn't a lot going on in this graph, mainly the absolute minimum point. So I would recommend something like [-200, 400] in order to show the (more or less) linear behavior of the function for both large positive and negative values of x.

-Dan
• May 20th 2006, 05:06 PM
diudiu
Hmm.. thank u for ure contributions ^^..

actually, i think i may have left out some valuable info.. its quite a long question but that equation represents the the total energy required by a moth to fly from A to C via B, Diagram in attatchment.

Though very much thanks to earboth, that's going to help in the next task.

So, would the domain still be the one you have calculated? :confused:
• May 20th 2006, 10:28 PM
CaptainBlack
Quote:

Originally Posted by diudiu
Hmm.. thank u for ure contributions ^^..

actually, i think i may have left out some valuable info.. its quite a long question but that equation represents the the total energy required by a moth to fly from A to C via B, Diagram in attatchment.

Though very much thanks to earboth, that's going to help in the next task.

So, would the domain still be the one you have calculated? :confused:

No now you are interested in $x \in [0,\sqrt{150^2-100^2}]$

RonL