Question
Asked Nov 12, 2019
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Determine if the curve is concave upwards or downwards at P(4,0).

t2, y t2 for -10 t 10
Consider the parametric
curve =
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t2, y t2 for -10 t 10 Consider the parametric curve =

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Expert Answer

Step 1

Consider the given parametric curve,

x f,y =t+2 for -10st10
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x f,y =t+2 for -10st10

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Step 2

To check the curve is concave upward or downward, find the second derivative that means d2y/dx2

dx
2t
dt
dy
=1
y t+2
dt
dy
dy
1
dt
dx
dx
2t
dt
d dy
dt dx
d y
dx
dx2
dt
1
dt 2t
2t
-1
1
2t2 2t
-1
4t
TT
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dx 2t dt dy =1 y t+2 dt dy dy 1 dt dx dx 2t dt d dy dt dx d y dx dx2 dt 1 dt 2t 2t -1 1 2t2 2t -1 4t TT

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Step 3

Now, find the value of t at the ...

Since, x f,yt2
Substitute x 4 and y 0
t=+2
and, y t 20 = t +2
t-2
So, common value,
t=-2
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Since, x f,yt2 Substitute x 4 and y 0 t=+2 and, y t 20 = t +2 t-2 So, common value, t=-2

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