Science:Math Exam Resources/Courses/MATH200/December 2012/Question 03 (b)
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Question 03 (b) 

Suppose that a function is implicitly deﬁned by an equation: (b) If , find the linear approximation of the function at . 
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Hint 

The linear approximation of a function at a point is

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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. What to do The linear approximation of a function in a point is
We have that . To find , we must solve the equation , where for the variable .
Hence, are solution to this equations. With the knowledge,that , the value must be
We already know from part a), that . Pluging in the point gives
We know that Pluging in the point gives
Hence the linear approximation is 