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Find an equation of the tangent line to the curve at the given point.

$ y = x^3 - 3x + 1 $, $ (2, 3) $

$y=9 x-15$

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So here we give an example of specific cubic function, let's say it has this sort of a shape and were given information that we're interested in the tangent line at the point. Let's call the point here 2:03. So the tangent line would be why I minus the value of the function at a certain point. So why minus Y. Of two would be equivalent to the derivative of the function at the X value times x minus The certain x value or interest in which the X -2. So this will give the equation of the tangent line. So we have function Y equals execute minus three X plus one. And if we take the derivative of this this would be equivalent to three X squared minus three. If we evaluate the derivative at the point X equals two, So be four times maybe four times 3, 12, 12 -3 is nine. So we'll be getting information. This would be rewriting this would be AY -3 Equals nine times x -2. And this means that Y equals nine x minus 18 plus three, which B nine x minus 15. And this is our final answer.

Johns Hopkins University