The function value and for all .

Differential notation of linear approximation: .

Estimate the value of .

Re-write the function.

.

Consider and .

Linear approximation : .

Find .

The derivative function .

Substitute in the function.

Substitute and in expression .

Estimate the value of .

Re-write the function.

.

Consider and .

Linear approximation: .

Substitute and in above expression.

The derivative function  .

is positive and increasing for all values of . 

This represents the tangent lines to the curve are more steep.

The tangent line is completely below the curve and the linear approximation gives an underestimate.

Therefore the results in part (a) are too small. 

(a) and .

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