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11 Nov 2021, 03:30
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Difficulty:
65%
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Question Stats:
48% (01:27) correct
52%
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wrong
based on 109
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Point P lies on the equation \(y= x^2 - 1\) and Point Q lies on the equation \(y= -x^2+1\). Find the difference between the minimum y coordinate value of Point P and the maximum y coordinate value of Point Q.
A. -2
B. -1
C. 0
D. 1
E. 2
A. -2
B. -1
C. 0
D. 1
E. 2
rvgmat12
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13 Nov 2021, 09:31
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Min y coordinate is -1 and max y coordinate is 1
Difference = -2
A
Posted from my mobile device
Difference = -2
A
Posted from my mobile device
13 Nov 2021, 09:39
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Given: Point P lies on the equation \(y= x^2 - 1\) and Point Q lies on the equation \(y= -x^2+1\).
Asked: Find the difference between the minimum y coordinate value of Point P and the maximum y coordinate value of Point Q.
For maxima and minima : -
dy/dx = 0
d2y/dx2 > 0 for minima
d2y/dx2 < 0 for maxima
Point P: -
\(y= x^2 - 1\)
dy/dx = 2x = 0 at x = 0
d2y/dx2 = 2 > 0 minima
At (0,-1) point P has a minima
Point Q: -
\(y= -x^2+1\)
dy/dx = -2x = 0 at x=0
d2y/dx2 = -2 < 0 maxima
At (0,1) point Q has a maxima
The difference between the minimum y coordinate value of Point P and the maximum y coordinate value of Point Q = -1 - (1) = -2
IMO A
Asked: Find the difference between the minimum y coordinate value of Point P and the maximum y coordinate value of Point Q.
For maxima and minima : -
dy/dx = 0
d2y/dx2 > 0 for minima
d2y/dx2 < 0 for maxima
Point P: -
\(y= x^2 - 1\)
dy/dx = 2x = 0 at x = 0
d2y/dx2 = 2 > 0 minima
At (0,-1) point P has a minima
Point Q: -
\(y= -x^2+1\)
dy/dx = -2x = 0 at x=0
d2y/dx2 = -2 < 0 maxima
At (0,1) point Q has a maxima
The difference between the minimum y coordinate value of Point P and the maximum y coordinate value of Point Q = -1 - (1) = -2
IMO A
