Differential Calculus

[darkphoenix]

Q1. Consider the curve

a) Find using implicit differentiation


I did it and got

Is that right?

[TrueTears]

hi-5 bro i got the same as u

[darkphoenix]

Cool thanks, just wanted to make sure.

[Mao]

You do realise a TI 89 (or higher) can do implicit differentiation.

[TrueTears]

i torrented mathematica recently, fark its powerful...

[darkphoenix]

Yeah i know, just wanted to triple check.

Anyway got another question (same questions as before, different part):

c) Find the equation of the normal to the curve at x=1

Cause when you sub in x=1 there is more than one point.

[TrueTears]

what values of y do u get after subbing in x = 1 into the equation of the graph?

[darkphoenix]

0 and 2?

[TrueTears]

well clearly 0 wont work right?

the dy/dx would be 'undefined'

but hmmm this could also mean its a vertical normal...

[darkphoenix]

Hm yeah true. Ok i used the point (1,2)

And i got the equation as y=2?

[darkphoenix]

Hey guys, heres another question:

Q3) The height, h metres, of a slow growing tree is modelled by the equation
(t is greater than or equal to 0)

c) When is the tree growing fastest?

Is this just finding the point of inflection? When ?

Cause i got for when its growing fastest, is that right?

EDIT: 700 Posts!

[moekamo]

yea you want to find when the rate of change of height with respect to time is greatest, ie when the double derivative is 0. Also you can see from the graph that at t=0 is when the gradient is greatest.

[darkphoenix]

Ok yeah cause when you think about it, it sounds weird, like the tree is growing its fastest at when no time has elapsed or something.

e) What will happen to the height of the tree eventually?

Is it that it will stop growing? Cause the graph approaches the asymptote

[moekamo]

it will approach a constant height value of .... metres or something along those lines

could also chuck in that as (I think thats the right value :S)

[darkphoenix]

Alright cool thanks again man.