Using directional derivative to find how fast the area of rectangle is changing?
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there is this problem in directional derivative chapter that I don't where to begin with.
A rectangle A(0,0), B(2,0), C(2,1), and D(0,1) sitting on xy plane. Point C is moving in the direction of vector V=<4,3> and the rest of points are fixed. How fast the area is changing? In what direction C must move to maximize the area? in what direction C can move without changing the area?
calculus partial-derivative
asked Jan 20 at 19:22
Andy LamAndy Lam
63
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add a comment |
$begingroup$
there is this problem in directional derivative chapter that I don't where to begin with.
A rectangle A(0,0), B(2,0), C(2,1), and D(0,1) sitting on xy plane. Point C is moving in the direction of vector V=<4,3> and the rest of points are fixed. How fast the area is changing? In what direction C must move to maximize the area? in what direction C can move without changing the area?
calculus partial-derivative
asked Jan 20 at 19:22
Andy LamAndy Lam
63
$endgroup$
$begingroup$
Forget the given coordinates of point $C$ for a moment. Given that it is a 'moveable' point, we can represent point $C$ by $(x,y)$, say. Can you work out an expression for the area in terms of $x$ and $y$?
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– Paul Aljabar
Jan 20 at 20:30
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So the function for area is xy and i take the partial derivative of xy to find gradient, multiply it to vector V, and then put point C in the result, right?
$endgroup$
– Andy Lam
Jan 20 at 22:11
add a comment |
$begingroup$
there is this problem in directional derivative chapter that I don't where to begin with.
A rectangle A(0,0), B(2,0), C(2,1), and D(0,1) sitting on xy plane. Point C is moving in the direction of vector V=<4,3> and the rest of points are fixed. How fast the area is changing? In what direction C must move to maximize the area? in what direction C can move without changing the area?
calculus partial-derivative
asked Jan 20 at 19:22
Andy LamAndy Lam
63
$endgroup$
there is this problem in directional derivative chapter that I don't where to begin with.
A rectangle A(0,0), B(2,0), C(2,1), and D(0,1) sitting on xy plane. Point C is moving in the direction of vector V=<4,3> and the rest of points are fixed. How fast the area is changing? In what direction C must move to maximize the area? in what direction C can move without changing the area?
calculus partial-derivative
calculus partial-derivative
asked Jan 20 at 19:22
Andy LamAndy Lam
63
asked Jan 20 at 19:22
Andy LamAndy Lam
63
asked Jan 20 at 19:22
Andy LamAndy Lam
63
asked Jan 20 at 19:22
Andy LamAndy Lam
63
asked Jan 20 at 19:22
Andy LamAndy Lam
63
63
$begingroup$
Forget the given coordinates of point $C$ for a moment. Given that it is a 'moveable' point, we can represent point $C$ by $(x,y)$, say. Can you work out an expression for the area in terms of $x$ and $y$?
$endgroup$
– Paul Aljabar
Jan 20 at 20:30
$begingroup$
So the function for area is xy and i take the partial derivative of xy to find gradient, multiply it to vector V, and then put point C in the result, right?
$endgroup$
– Andy Lam
Jan 20 at 22:11
add a comment |
$begingroup$
Forget the given coordinates of point $C$ for a moment. Given that it is a 'moveable' point, we can represent point $C$ by $(x,y)$, say. Can you work out an expression for the area in terms of $x$ and $y$?
$endgroup$
– Paul Aljabar
Jan 20 at 20:30
$begingroup$
So the function for area is xy and i take the partial derivative of xy to find gradient, multiply it to vector V, and then put point C in the result, right?
$endgroup$
– Andy Lam
Jan 20 at 22:11
$begingroup$
Forget the given coordinates of point $C$ for a moment. Given that it is a 'moveable' point, we can represent point $C$ by $(x,y)$, say. Can you work out an expression for the area in terms of $x$ and $y$?
$endgroup$
– Paul Aljabar
Jan 20 at 20:30
$begingroup$
Forget the given coordinates of point $C$ for a moment. Given that it is a 'moveable' point, we can represent point $C$ by $(x,y)$, say. Can you work out an expression for the area in terms of $x$ and $y$?
$endgroup$
– Paul Aljabar
Jan 20 at 20:30
$begingroup$
So the function for area is xy and i take the partial derivative of xy to find gradient, multiply it to vector V, and then put point C in the result, right?
$endgroup$
– Andy Lam
Jan 20 at 22:11
$begingroup$
So the function for area is xy and i take the partial derivative of xy to find gradient, multiply it to vector V, and then put point C in the result, right?
$endgroup$
– Andy Lam
Jan 20 at 22:11
add a comment |
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$begingroup$
Forget the given coordinates of point $C$ for a moment. Given that it is a 'moveable' point, we can represent point $C$ by $(x,y)$, say. Can you work out an expression for the area in terms of $x$ and $y$?
$endgroup$
– Paul Aljabar
Jan 20 at 20:30
$begingroup$
So the function for area is xy and i take the partial derivative of xy to find gradient, multiply it to vector V, and then put point C in the result, right?
$endgroup$
– Andy Lam
Jan 20 at 22:11