Find the points on the lemniscate 2(x^2 + y^2)^2 = 25(x^2 - y^2) where the tangent is horizontal. The derivative using implicit differentiation is (-4x^3 - 4xy^2 + 25x)/(4x^3 + 4x^2 y + 25y)
2 answers:
Hello,
You got this
4(x^2 + y^2)(2x - 2yy') = 25(2x - 2yy')
I think the 2nd factor on the left-hand side should be (2x+2y y'). So it should be
4(x^2 + y^2)(2x + 2yy') = 25(2x - 2yy')
Now solve for y'
you get
<span><span>y′</span>=<span><span>−4<span>x3</span>−4x<span>y2</span>+25x</span><span>25y+4y(<span>x2</span>+<span>y2</span>)</span></span>=0</span>
<span>
It looks like we can solve the numerator for the x values that make it zero.</span>
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