Science:Math Exam Resources/Courses/MATH100/December 2010/Question 01 (i)/Solution 1
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Let ƒ (x)=x1/3. First we need a number a as close to 30 as possible but whose cube root we know. A good candidate would be 27, because 33=27 and so .
We know that the general formula for a linear approximation is given by
We can find the derivative:
Knowing these values, we can plug them in to the linear approximation equation and find the approximation for x=30, using a=27:
So using linear approximation,