(a)

The curve is  and point is .

Consider .

Apply derivative on each side with respect to .

Derivative of secant function : .

.

Slope of the tangent line is derivative of the function at .

Substitute  in the derivative function.

.

Slope of the tangent line to the curve at the point  is .

Find the tangent line.

Point-slope form of line equation : .

Substitute  and  in point-slope form.

The tangent line is .

(b)

Graph :

Graph the function and tangent line passing through the point.

Observe the graph.

The tangent line is  touches the curve at .

(c)

Graph :

Graph the function and tangent line passing through the point using derivative feature.

Observe the graph.

The slope of the tangent line to the curve at the point  is .

(a) The tangent line is .

(b) Graph of the function and tangent line passing through the point is

(c) Graph of the function and tangent line passing through the point using derivative feature is

.