Hi there. Bit of a headscratcher here. I am perplexed by part (c) of the attached question.
I understand that if the tangent makes an angle of pi/4 with the horizontal axis, this is equal to a gradient of 1. When I plug this into the value of dy/dx I worked out, I come out with the same co-ordinates as those in part b) ! This surely can't be.
my answer to part a) : dy/dx = (2x - y) / (x + 1 - 2y)
part b) stationary when 2x - y = 0, therefore sub y = 2x into first equation, and you come out with a quadratic 3x^2 - 2x -1 = 0 and this solves for x is -1/3 or + 1
then c) as dy/dx is equal to 1, then 2x - y = x + 1 - 2y
this re-arranges to y = 1 -x however when you sub that in you get the same quadratic as b) , please help!
I understand that if the tangent makes an angle of pi/4 with the horizontal axis, this is equal to a gradient of 1. When I plug this into the value of dy/dx I worked out, I come out with the same co-ordinates as those in part b) ! This surely can't be.
my answer to part a) : dy/dx = (2x - y) / (x + 1 - 2y)
part b) stationary when 2x - y = 0, therefore sub y = 2x into first equation, and you come out with a quadratic 3x^2 - 2x -1 = 0 and this solves for x is -1/3 or + 1
then c) as dy/dx is equal to 1, then 2x - y = x + 1 - 2y
this re-arranges to y = 1 -x however when you sub that in you get the same quadratic as b) , please help!
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