# Science:Math Exam Resources/Courses/MATH101/April 2017/Question 04 (b)/Solution 1

Using the information given above all we need to find is and replace the values of in the formula for the error , as the difference between the 2 numbers will, at most, be the error.

Thus we must first find the 2nd derivative of :

.

We must now bound the derivative. Using the inequatility , we have:

. Furthermore we know that , and, in our domain, , which makes us conclude that on . (Note that this does not necessarily mean the maximum of is . The value is only an *upper bound*; other bounds are possible.)

Thus the difference is given by

**Answer:** (note that this is only one possible answer; see the note above)