(a)

The function is .

Observe the graph .

Find the slope of the tangent line.

Slope of a tangent line with points  and  : .

Consider two points on the tangent line as  and .

Slope of  tangent line with points  and  and : .

Slope of the tangent line to the curve  is .

(b)

The function is .

Observe the graph .

Find the slope of the tangent line.

Slope of a tangent line with points  and  : .

Consider two points on the tangent line as  and .

Slope of  tangent line with points  and  and : .

Slope of the tangent line to the curve  is .

Verification:

(a)

The function is .

Find the slope of the tangent line.

Slope of the tangent line is the derivative of the function at a particular point.

Apply derivative on each side with respect to .

Apply power rule of derivatives : .

Substitute  in the .

Slope of the curve is .

Slope of the tangent line to the curve  is .

Verification:

(b)

The function is .

Find the slope of the tangent line.

Slope of the tangent line is the derivative of the function at a particular point.

Apply derivative on each side with respect to .

Apply power rule of derivatives: .

Substitute  in the .

Slope of the curve is .

Slope of the tangent line to the curve  is .

(a) Slope of the tangent line to the curve  is .

(b) Slope of the tangent line to the curve  is .