Step 1 :

(a)

The function is .

The slope of the tangent line is equal to the derivative of the function.

Differentiate the function with respect to . 

Apply power rule of derivatives :

.

At , .

The slope of the tangent to the curve at is 12.

Step 2 :

(b)

The function is .

The slope of the tangent line is equal of the derivative of the function.

Differentiate the function with respect to . 

.

Apply power rule of derivatives : .

.

At ,

The slope of the tangent of the curve at is .

Step 3 : 

(c)

The function is .

The slope of the tangent line is equal of the derivative of the function.

.

Differentiate the function with respect to . 

.

Apply power rule of derivatives : .

.

At , .

The slope of the tangent of the curve at is .

Solution :

(a) The slope of the tangent to the curve at is 12.

(b) The slope of the tangent of the curve at is .

(c) The slope of the tangent of the curve at is .