Problem: Find the tangent line and the normal line at a = 1 to the graph of the function

Solution: We are looking for a line that goes through the point (a, f (a)) = (1,3). The equation of such a line is

y − f (a) = k⋅(x − a).

To get a tangent line we use the slope k_T = f ′(a). First we find the derivative of f.

Thus k_T = f ′(1) = 19/3. The equation of the tangent line is

The slope of the normal line is given by the formula

Thus the equation of the normal line is

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