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Problem 39 Medium Difficulty

Fidn an equation of the tangent line to the curve at the given point. Illustrate by graphing the curve and the tangent line on the same scree.
$ y = 3x^2 - x^3, (1,2) $

Answer

$$y^{\prime}=6 x-3 x^{2}$$

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Video Transcript

Hey, it's Claire. So when you married here. So we have. Why is equal to three X square minus X cubed? We're gonna find the derivative. Do you lie over DX? This is equal to D six X minus three X square when we plug in one to get three. Why minus two is equal to three X minus one point slope form. We get three X minus one or our tangent line. So here we have our crab. Why, thanks. And we're gonna first graph aren't 100 line. So at Cerro, it's gonna be negative one. And at one, it's gonna be two. So this is art. Ancient line, then Original has Ah, it crosses the origin. It has a 0.24 goes above here and goes back down. So look something like this.