(a) .

Approximate a tangent line to the given curve at the point .

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

Draw the tangent line at .

Observe the graph.

The tangent line passes through the points  and .

Slope of the tangent line at  is .

(b) .

Approximate a tangent line to the given curve at the point .

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

Draw the tangent line at .

Observe the graph.

Since the tangent line is horizontal, .

Slope of the tangent line at  is .

(c) .

Approximate a tangent line to the given curve at the point .

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

Draw the tangent line at .

Observe the graph.

The tangent line passes through the points  and .

Slope of the tangent line at  is .

(d) .

Approximate a tangent line to the given curve at the point .

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

Draw the tangent line at .

Observe the graph.

The tangent line passes through the points  and .

Slope of the tangent line at  is .

(e) .

Approximate a tangent line to the given curve at the point .

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

Draw the tangent line at .

Observe the graph.

The tangent line passes through the points  and .

Slope of the tangent line at  is .

(f) .

Approximate a tangent line to the given curve at the point .

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

Draw the tangent line at .

Observe the graph.

Since the tangent line is horizontal, .

Slope of the tangent line at  is .

(g) .

Approximate a tangent line to the given curve at the point .

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

Draw the tangent line at .

Observe the graph.

The tangent line passes through the points  and .

Slope of the tangent line at  is .

Make table for the slopes of these lines for given values of x :

Graph :  

1) Draw the co-ordinate plane.

2) Plot the points obtained in the above table.

3) Connect the points with a smooth curve.

Graph of differential function is :

(a) 

(b) 

(c) 

(d) 

(e) 

(f) 

(g) 

Graph of differential function is :

.