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Numerade Educator

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Problem 61 Medium Difficulty

Find an equation of the normal line to the curve $ y = \sqrt{x} $ that is parallel to the line $ 2x + y = 1. $

Answer

When $x=1, y=\sqrt{1}=1$, equation of the normal line is $y-1=-2(x-1)$ or$y=-2 x+3$

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Video Transcript

feuds Clear. So when you're in here so we have two X plus. Why is equal to one? We're gonna find slow. I sleep. Why? Why equals negative two X plus one on our slope is negative too. And then we get why is equal to the square root of X refunding the equation of the tension line of the given curve which is equal to X to the 1/2 power. The derivative is equal to one over two square root of X. Then we're gonna find a normal line which is negative to square root of X. This is shown when we use negative one over the derivative. Then we do Negative two squared of X is equal to negative too. We're just gonna find for X and Y X equals one. And why is equal to half of one which is equal to one? Then we're going to find the equation. This is lye minus one is equal to negative too. X minus one. Why is equal to negative two x plus three