Question

@sat

Answer 1

Saifoo?

Answer 2

Yasmine?

Answer 3

Yeah, it's me. :)

Answer 4

@spam

Answer 5

and it's me as well. :)

Answer 6

Haha

Answer 7

^_~

Answer 8

hi

Answer 9

I see medal rain coming.

Answer 10

Hi saiff:D:D

Answer 11

Hey crazymom! how are you??

Answer 12

loooool :@

Answer 13

@GT bhai and Tom, lol. no i wanted to ask a question from Sat.

Answer 14

@lulu!!!!! =D

Answer 15

@Saifoo - Yes!

Answer 16

@yas, hmmm.. i thought so..

Answer 17

welcome sat. :)

Answer 18

i wanted to ask you, like in the last question, what if we have 2 and 5.. then what we gonna do?

Answer 19

??

Answer 20

http://assets.openstudy.com/updates/attachments/4f08fc1fe4b014c09e63f28d-saifoo.khan-1325988921584-img20120108wa0000.jpg

Answer 21

we just did that right?

Answer 22

in this case, we used dy/dx and estimated the change.. of 2 and 2.01

what if we had like numbers 2 and 5

Answer 23

well then your estimate would suck

Answer 24

lol

Answer 25

you are trying to estimate the derivative, the slope of the tangent line. you want to pick numbers that are close together, not 3 units apart!

Answer 26

the slope of the secant line would be
\[\frac{f(5)-f(2)}{3}\] but it would probably not be very near
\[f'(2)\]

Answer 27

Ok, what if we aren't "estimating" then?

Answer 28

solve using dy/dx man!

Answer 29

not sure what you mean exactly. if you want the "real answer" take the derivative and replace it by the number

Answer 30

so in your example here,
\[y=x^3,y'=3x^2\] and so the slope at x =2 is
\[3\times 2^2=12\] which is why you got a decent estimate when you used 2 and 2.01

Answer 31

what if we have to find the slope b/w point 2 and 5?
like x=2 and x=5 using the same equation y=x^3

Answer 32

yes you would get
\[\frac{5^3-2^3}{3}\]