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 ..

2. 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,

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

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 $\displaystyle \mathbb{R}$

What bothers me a little bit is: Why do you believe that the domain is $\displaystyle 0<x<\sqrt{12500}$

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

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

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

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

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

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

E(57.735) = 285.0085

Greetings

EB

3. 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

4. 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?

5. 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?
No now you are interested in $\displaystyle x \in [0,\sqrt{150^2-100^2}]$

RonL