Drawing a functin given the derivative (1 Viewer)

[rama_v]

Drawing a function given the derivative

Can anyone please explain to me the proper method for drawing a graph given the graph of the derivative? For example:

(I have attached a copy of teh graph y=f'(x))
"USe this graph to draw the graph of f(x) given that the range of f(x)>0"

Thanks

 

[shafqat]

Can anyone please explain to me the proper method for drawing a graph given the graph of the derivative? For example:

(I have attached a copy of teh graph y=f'(x))
"USe this graph to draw the graph of f(x) given that the range of f(x)>0"

Thanks

where the derivative is 0, there is a critical pt
then u have to look at the sign either side of the zero to determine its nature
in this case the signs are + 0 -, so there is a max
the derivate approaches 0 on either side, so there would be horizontal asymptotes
when the derivate has max and min, there is a pt of inflexion
and remember if they dont give u a point on the graph, then there can be more than one possible solution (infinitely many) because of the constant + c

 

[Slidey]

Uh. I thought that was 4unit? Bet you $100 you'll never be asked that in the HSC.

But yeah...

f(x) has a stationary pt at x=0.

As x-> -infinity, f(x) gets more shallow with positive concavity
As x-> infinity, f(x) gets more shallow with negative concavity.

There's probably other tricks. Can't remember.

Maybe f(x) looks like a bell curve with an asymptote at x=0?

EDIT: What shafqat said.

 

[rama_v]

Thansk....So would the solution to teh graph be similar to this graph? Btw we got asked this question in a 2 unit exam today...

 

[shafqat]

thats it...

 

[Slidey]

From a quick inspection, that's what I'd say it looks like... but I haven't done curve sketching in a while.

 

[rama_v]

Cool, thanks for your help

 

[FinalFantasy]

Uh. I thought that was 4unit? Bet you $100 you'll never be asked that in the HSC.

But yeah...

f(x) has a stationary pt at x=0.

As x-> -infinity, f(x) gets more shallow with positive concavity
As x-> infinity, f(x) gets more shallow with negative concavity.

There's probably other tricks. Can't remember.

Maybe f(x) looks like a bell curve with an asymptote at x=0?

EDIT: What shafqat said.

give me $100 now!
there's a q. where ur given f'(x) and u have to draw f(x) in the 2unit maths HSC paper year 2000, question 9B

 

[Slidey]

That was an cent sign, but sure.

 

[sunjet]

lol questions like that always pop up there are 4 rules i study but im too tired to go get my book