Science:Math Exam Resources/Courses/MATH110/April 2011/Question 04 (c)
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Question 04 (c) 

Given a curve, its curvature K is a measure of how much it deviates from a straight line. It can be computed using the following formula: In this question you will calculate the curvature of the curve x^{4} + y^{4} = 2 at a certain point. Find the curvature K of the curve at the point (1,1). 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Try solving for the numerical values of and before plugging them into the formula for curvature. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. It will be complicated to simply plug our expressions for and into the formula for curvature. Instead it might be wiser to calculate the actual value of and at the point . For we have And for we have Plugging these values of and into the formula for K we get:
