The function value is .

Differential notation of linear approximation: .

Estimate the value of .

Re-write the function.

.

Consider  and .

Linear approximation: .

From the graph, .

Substitute  and  in above expression.

Estimate the value of .

Re-write the function.

.

Linear approximation: .

Substitute  and  in above expression.

(b)

Observe the graph.

 is positive and decreasing.

The curve is above the derivative of the function.

The tangent line is completely above the curve and the linear approximation gives an overestimate.

Therefore, the results in part (a) are too large. 

(a)  and .

(b) Estimates in part (a) are too large.