Maximum and Minimum Value Application question

shanshan
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Homework Statement


Find the value of k if the function y=x^2+kx+72 has a local minimum at x=4
 
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What have you tried for this problem.
 
Differentiate the original function and you get y = 2x + k ,and it has a local minimun at x=4.
Block 4 in and the output(y) should be 0 because of Fermat's theorem (http://en.wikipedia.org/wiki/Fermat's_theorem_(stationary_points))

So you'll get k = -8 ,is that correct ?
 
yes! thankyou so much :)
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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