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Problem 59 Medium Difficulty

Find equation of both lines that are tangent to the curve $ y = x^3 - 3x^2 + 3x - 3 $ and are parallel to the line $ 3x - y = 15. $

Answer

Points on the curve are (0,-3) and (2,-1). tangent line equations are $y-(-3)=3(x-0)$ or $y=3 x-3$ and $y-(-1)=3(x-2)$ or $y=3 x-7$

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Video Transcript

it's clear. So when you married here you can write three X minus Y equals 15 as why is equal to three X minus 15. Then this is equal to em. You differentiate our function, we got Do I over DX is equal to three x square minus six x plus three. Three is equal to three X square minus six X plus three. When we get X, I'm X minus two is equal to zero. So X has to be equal to zero or two. When Xs equal to zero, we have a why Volume two So the tangent passes through zero common negative three. The equation of the tension is why equals three X minus three access equal to two. Then we have to calm a negative one. So the equation off the tangent becomes why is equal to three X minus seven.