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

$ y = 4x - 3x^2 $, $ (2, -4) $

$y=-8 x+12$

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Missouri State University

Oregon State University

University of Michigan - Ann Arbor

Idaho State University

So in this problem, were given this equation of problem, why equals four x minus three X squared. And asked to find the equation of the tangent line. It goes through the point to -4. We know that the tangent line will have the slope at this X. Value on this on this curve on this function. So find the derivative which is the slope of the tangent line at that at that the value of the curve which is, so at this point on the on this curve the slope of the tangent line will have Slope based on the derivative of this. The derivative of this is four six X. So then we evaluate that at two 4 -12 which is -8. And now I have a point and I have the slope. So using the point slope formula why minus Y. One equals m times x minus x. One, I have y minus a negative four Is equal to -8 times X -2. So this is why equals negative eight X distributing the negative eight, -8 times negative two is positive 16 Negative Times -4 is positive for. But then you subtract it to get to the side. So that's 16 -4 which is 12. Well this is plus 12. There is the equation of our line tangent to this curve at that point on the curve

Oklahoma State University