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(a)
The curve is and the point is .
Definition of the absolute function:
If , then .
If , then .
Rewrite the function in piecewise function form.
We need to determine the tangent line at .
Here .
Consider .
Differentiate on each side with respect to .
Quotient rule of derivatives:.
Slope of the tangent is derivative of the function.
Slope at of the tangent line at
Determination of the tangent line:
Point-slope form: .
Substitute and in the above formula.
Equation of the tangent line is .
(b)
Graph of the function and the tangent line
(a) Equation of a tangent line .
(b) Graph of the function and the tangent line.
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