# Curvature calculation

Find the curvature at the point P:

f : [0;2] IR^2 , f (t) = 2t,4 −2t^3 , P(2,2)

i subs 2x=0 then x=0 and 2y=2 then y=1

t=(0,1)

then i perform the curvature calculation.however,i'm confuse that in this case i have to subs t=1 to get a value instead of zero.
If the value t=(2 ,3) or others, which one should i choose??

## Answers and Replies

HallsofIvy
Homework Helper
teng125 said:
Find the curvature at the point P:

f : [0;2] IR^2 , f (t) = 2t,4 −2t^3 , P(2,2)

i subs 2x=0 then x=0 and 2y=2 then y=1
Why substitute 2x= 0? Since x= 2 at P, you should have
x= 2t= 2 so t= 1. Unfortunately, if t= 1 then y= 4 -2(2)3= 4- 16= -12, not 2. Are you sure you have copied the problem correctly? (2,2) is not on the curve f(t)= (2t, 4- 2t3)!

t=(0,1)
What does this mean? t is number, not an interval or a set.

then i perform the curvature calculation.however,i'm confuse that in this case i have to subs t=1 to get a value instead of zero.
If the value t=(2 ,3) or others, which one should i choose??
Again, I don't know what you mean by "t= (2, 3)". As I said before, this problem is stated incorrectly. The point (2,2) is not on the curve f(t)= (2t, 4- 2t3).

but the problem stated P(2,2)

VietDao29
Homework Helper
HallsofIvy said:
Why substitute 2x= 0? Since x= 2 at P, you should have
x= 2t= 2 so t= 1. Unfortunately, if t= 1 then y= 4 -2(2)3= 4- 16= -12, not 2. Are you sure you have copied the problem correctly? (2,2) is not on the curve f(t)= (2t, 4- 2t3)!
Uhmm, in fact, (2, 2) is on the curve, since:
x = 2t = 2 <=> t = 1
Plug t = 1 in, we have: y = y= 4 - 2(1)3 (It's 1, not 2 ) = 2.
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@teng125:
Ok, open up your textbook, or notes. Can you find the formula to find the curvature of a curve given parametrically?

HallsofIvy
Homework Helper
VietDao29 said:
Uhmm, in fact, (2, 2) is on the curve, since:
x = 2t = 2 <=> t = 1
Plug t = 1 in, we have: y = y= 4 - 2(1)3 (It's 1, not 2 ) = 2.
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Well, we can just kind of ignore that, can't we! :uhh: :uhh:

@teng125:
Ok, open up your textbook, or notes. Can you find the formula to find the curvature of a curve given parametrically?

HallsofIvy