Defining the Derivative and Using Derivative Notation

Question

Find the tangent and normal line for the function: 

at x= -2.  Then graph the function and the tangent line.  Be sure to show all work and correct notation!! 

Answer 1

The tangent line equation is y-f(2) = f'(2)(x+2)

f'(x) = -4/x² so f(-2) = -2 and f'(2) = -1

y+2 = -(x+2) or y = -x - 4

The normal line will be the line perpendicular to the tangent: slope of 1 through the point (-2,-2)

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