anonymous one year ago ..

1. anonymous

I think the right answer to this is .12

2. zepdrix

So for linear approximation we use ummm...$\large\rm f(x)\approx f(x_o)+\color{orangered}{f'(x_o)(x-x_o)}$Something like that, ya? Where the orange stuff is our error. Wait.. is that the error? Hmmm thinking

3. anonymous

Im not sure this problem is very confusing

4. zepdrix

Yes it is +_+ So the error in the output $$\large\rm \Delta y$$ ummm... ya ya ya, should be $$\large\rm f'(x_o)\color{green}{\Delta x}$$, where Delta x is the distance between our base point x_o and x. $$\large\rm \Delta y\approx f'(x_o)\color{green}{(x-x_o)}$$ So our base point is x=1. And we're drifting 0.001 away from that. $\large\rm \Delta y\approx f'(1)(0.001)$

5. zepdrix

Were you able to come up with a formula for Surface Area of a cube? :) And its derivative?

6. anonymous

No I was not

7. zepdrix

Take a cube, call the side length x. Since it's a cube, all side lengths are the same. The area of one face will be x*x, ya? So the total surface area will be the area of all 6 panels of the cube. $$\large\rm A=6x^2$$

8. zepdrix

Wait wait, then how were you able to come up with .12? LOL Just straight up guessing? >.< Buhaha, Cam cam, come on!!

9. anonymous

Haha yes it was a guess but it made sense

10. zepdrix

So your derivative is $$\large\rm A'=12x$$. Mmm k.

11. zepdrix

And your error approximation for the output $$\large\rm \Delta y$$ is going to be$\large\rm =A'(x_o)\Delta x$Our base point is x=1. And our delta is the distance between the x's, 0.001.

12. anonymous

Ok

13. zepdrix

$\large\rm =A'(1)(0.001)=?$

14. anonymous

1X10^-3

15. zepdrix

What? 0_o Plug 1 into A'(x) and then multiply that value by 0.001

16. anonymous

Oooo .12?

17. zepdrix

Hmm that's not what I'm getting.. lemme see..

18. zepdrix

$\large\rm =\color{orangered}{A'(1)}(0.001)=\color{orangered}{12(1)}(0.001)=12(0.001)=0.012$

19. zepdrix

Is that one of our options? :o Hopefully we're doing this right <.<

20. anonymous

Yes it is!!

21. anonymous

Wait no its .12

22. zepdrix

What do the other options look like? XD

23. anonymous

.02 .003 and none of the above

24. zepdrix

Hmm :p @ganeshie8 @dan815

25. anonymous

Ill just put in .12 and hope thats the answer

26. anonymous

Thank you for the help!

27. zepdrix

ya sorry :c

28. anonymous

Its okay thanks for the help!!