SOLUTION: The line 5x-5y=2 touches the curve x^2y-5x+y+2=0, find the coordinates of the points of intersection. Find the gradient at each of the points
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-> SOLUTION: The line 5x-5y=2 touches the curve x^2y-5x+y+2=0, find the coordinates of the points of intersection. Find the gradient at each of the points
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Question 1161693: The line 5x-5y=2 touches the curve x^2y-5x+y+2=0, find the coordinates of the points of intersection. Find the gradient at each of the points Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! The line 5x-5y=2 touches the curve x^2y-5x+y+2=0, find the coordinates of the points of intersection. Find the gradient at each of the points
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5x-5y=2
Solve for y
y = (5x-2)/5
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x^2y-5x+y+2=0
Sub for y
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x^2*(5x-2)/5 - 5x + (5x-2)/5 + 2 = 0
Multiply by 5
x^2*(5x-2) - 25x + (5x-2) + 10 = 0
5x^3 - 2x^2 -20x + 8 = 0
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Solve for x
x = 2 is a root
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x = -2 is a root
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x = 0.4 is a root
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f(x) = 5x^3 - 2x^2 -20x + 8
f'(x) = 15x^2 - 4x - 20
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Sub for x at the 3 roots and find the 3 slopes.
