(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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