Tangent line problem

FINDING THE EQUATION OF THE TANGENT LINE TO A CURVE

In order to find the equation of the tangent line to the curve at a given point you  need two things: 1) the slope of the line at that point, and 2) the (x1, y1) coordinates of the particular point.  Typically you are given the function and the x1 value where you want the tangent line to touch the curve.

By taking the derivative of the original function, you get another function of x.  By subsituting the given value of x, which we are calling x1, into the derivative function, you can find the value of the slope of the tangent line at that point.  We call the value of the slope m.

You then have to find the y value that corresponds to the given x1, which we are calling y1.  To do that, you substitute x1 into the original given function to get the y1 value that corresponds to that given x1.

You now have the slope of the tangent line, and a point the line goes through.  By substituting into the following equation of the straight line you get the equation of the tangent line at point (x1, y1).

(y-y1) = m (x-x1)  You can leave your answer in that form.

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