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Draw a diagram showing two perpendicular lines that intersect on the $y$-axis and are both tangent to the parabola $y=x^2$. Where do these lines intersect?

    Draw a diagram showing two perpendicular lines that intersect on the $y$-axis and are both tangent to the parabola $y=x^2$. Where do these lines intersect?
Single Variable Calculus: Early Transcendentals
Single Variable Calculus: Early Transcendentals
James Stewart,… 9th Edition
Chapter 3, Problem 89 ↓
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Draw a diagram showing two perpendicular lines that intersect on the $y$-axis and are both tangent to the parabola $y=x^2$. Where do these lines intersect?
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Transcript

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00:02 So why most x square? so you can try to find two tension line that intercept perpendicular thiss this graph look symmetric so i kind of assumed that if this tension lines has a point, actually host this one should be and actually most negativity.
00:36 So if you have x e t good, so the other point should be ex he was never fifty by most square self example this point.
00:49 Hey, this is point being.
00:53 We're trying to find the question of the tension line the equation.
00:57 First of all, let's try to figure out slope the slope is shooting.
01:04 Despues the y prime me most to x on.
01:07 This will tell you the slow no so slow off this tension line that passed through the point eight should be on shooting.
01:20 And here the slope should be active duty.
01:26 And because if they're if they're proper different to each other, this product, the slope should be attentive.
01:31 One some primitive means a product.
01:34 They're so which is that that you're forty square should be one.
01:40 So that tell us, tio no.
01:46 So so i should be negative one, particularly the product of a slope should be that one so that he tells he was prosser minus one over two.
01:58 So here's how the point, eh? will be won over to one over.
02:04 Foreign point b will be nephew fund over two and one over four.
02:09 Now, where do this'll i intercept.
02:13 So we already have on the slope of the off this line will be one...
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