Use Local Linearization to Determine Whether or Not $y = \frac { 1 } { 4 } x + 1$

question 106

Essay

Use local linearization to determine whether or not $y = \frac { 1 } { 4 } x + 1$ provides a good estimate of $f ( x ) = \sqrt { x }$ for values of x near 4.If it does not, then determine a better linear approximation.If it does provide a good approximation, use it to estimate $\sqrt { 4.008 }$ .