http://www.freeimagehosting.net/7kphi
yup I was too lazy so I took a screenshot of my hw and uploaded it, please take a look this is the ONLY problem that I cannot do by myself like wtf its so hard. I know you start doing that dy/dx thing but then when you subsitute I get lost, like idk what you substiute for what
Anywho who got all the correct answers (both x values) -- why are there two x's not y's? Confused. And fill in the blanks at the end..if anyone can get all correct answer youll make me one very happy girl and get 10 points for you ;) thanks x1000!
yup I was too lazy so I took a screenshot of my hw and uploaded it, please take a look this is the ONLY problem that I cannot do by myself like wtf its so hard. I know you start doing that dy/dx thing but then when you subsitute I get lost, like idk what you substiute for what
Anywho who got all the correct answers (both x values) -- why are there two x's not y's? Confused. And fill in the blanks at the end..if anyone can get all correct answer youll make me one very happy girl and get 10 points for you ;) thanks x1000!
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19x² + xy + 3y = 2
y(x + 3) = 2 − 19x²
y = (2 − 19x²) / (x + 3)
dy/dx = (−38x(x + 3) − (2−19x²)(1)) / (x + 3)²
........ = (−38x² − 114x − 2 + 19x²) / (x + 3)²
........ = (−19x² − 114x − 2) / (x + 3)²
Tangent line is horizontal when dy/dx = 0
−19x² − 114x − 2 = 0
19x² + 114x + 2 = 0
x = (−114 ± √(114²−4(19)(2))) / (2*19)
x = (−114 ± √12844) / (2*19)
x = (−114 ± 2√3211) / (2*19)
x = (−57 ± √3211) / 19
x = (−57 + √3211) / 19 and x = (−57 − √3211) / 19
x = −0.01759546 and x = −5.98240454
Since there are "2" real solutions, there are "2" horizontal tangents
I'm not sure why they don't ask for y's, since original question asks for both coordinates of all points. But to find y-coordinates, just plug x values into function:
x = −0.01759546
y = (2 − 19(−0.01759546)²) / (−0.01759546 + 3) = 0.668627468
x = −5.98240454
y = (2 − 19(−5.98240454)²) / (−5.98240454 + 3) = 227.3313725
y(x + 3) = 2 − 19x²
y = (2 − 19x²) / (x + 3)
dy/dx = (−38x(x + 3) − (2−19x²)(1)) / (x + 3)²
........ = (−38x² − 114x − 2 + 19x²) / (x + 3)²
........ = (−19x² − 114x − 2) / (x + 3)²
Tangent line is horizontal when dy/dx = 0
−19x² − 114x − 2 = 0
19x² + 114x + 2 = 0
x = (−114 ± √(114²−4(19)(2))) / (2*19)
x = (−114 ± √12844) / (2*19)
x = (−114 ± 2√3211) / (2*19)
x = (−57 ± √3211) / 19
x = (−57 + √3211) / 19 and x = (−57 − √3211) / 19
x = −0.01759546 and x = −5.98240454
Since there are "2" real solutions, there are "2" horizontal tangents
I'm not sure why they don't ask for y's, since original question asks for both coordinates of all points. But to find y-coordinates, just plug x values into function:
x = −0.01759546
y = (2 − 19(−0.01759546)²) / (−0.01759546 + 3) = 0.668627468
x = −5.98240454
y = (2 − 19(−5.98240454)²) / (−5.98240454 + 3) = 227.3313725
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