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Let P be a point on the graph of y x The tangent line at...

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Calculus

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Let P be a point on the graph of y x The tangent line at P will intersect the graph at the point Q a If P has x coordinate a then what is the equation of the tangent line at P y x b The line in a will intersect the curve y x in two places one of these is P and the other point is Hint This part involves factoring a cubic in x In general this may be difficult However in this case since we know point P is an intersection point x a must be a solution so x a must be a factor You should now be able to f c The ratio of the slope of the curve at Q to the slope at P is

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