Question

Help needed with differentiation!

Answer 1

Can you differentiate 3t^2?

Answer 2

6t?

Answer 3

Yep, can you differentiate sqrt(y)?

Answer 4

(1/2)y^(-1/2).

Answer 5

Can you use the chain rule to differentiate sqrt(2-t) then?

Answer 6

Yes, I can get to the point where I get dq/dt. But what I'm having trouble is is the next part of the question - How do I find t for when i is max? How do I find what i_max is, to begin with?

Answer 7

To find extrema, you differentiate it again and set it equal to 0

Answer 8

that is di/dt=0

Answer 9

I see... Then how do I justify it, then?

Answer 10

Then you need to differentiate it again (three times you differentiate) and put the value of t when di/dt=0 to the further differentiated expression and see if it is positive or negative.

Answer 11

If it is positive, the slope is increasing and it's the minimum.
If it is negative, the slope is decreasing and it's the maximum.

Answer 12

Because di/dt is the slope of t, and when you differentiate it again it'll be the slope of slope.

Answer 13

Meaning after I sub t in, then look at the sign to determine whether it's max or min?

Answer 14

You substitute the value of t to the thrice-differentiated expression.

Answer 15

That means, put the value of t when di/dt=0 into d^2i/dt^2

Answer 16

Ah... I get it. Thanks again!

(My exams are tomorrow, so you all are really being a great help. If I manage to do well, it'll be all thanks to the guys here!)

Answer 17

Sorry I can't fan you again. :P

Answer 18

No problem at all, feel free to ask more questions if you have :)

Answer 19

Your Japanese name is 桐野嵐 expressed in kanji?

Answer 20

Aha, it's actually supposed to mean "Kiri naka no arashi", or "storm inside the mist". It's a nickname I had a few years back, but I've stuck with it till now, lol.

Answer 21

Then what's your name? :)

Answer 22

Tyler. I have a bit too much obsession with anime and manga, so yeah, lol.

Answer 23

oh i see