Given that y = 16x + 1/x , find the two values of x for which dy/dx = 0
The first stage of this question involves differentiating the equation of y in terms of x given to us. In order to differentiate, we first need to write y in terms of base x (where all the terms are x to the power of n). 1/x will go to x-1. Now we can differentiate for each term in the equation, bringing the power for each value of x down and multiplying it by the coefficient of the term, and then reducing the power of x by 1. This gives an equation for dy/dx = 16 - 1/x2.
The second stage of the question involves solving the dy/dx equation to get values of x for which dy/dx = 0. By putting our equation for dy/dx = 0 and solving it for x, we will get two values for x, which is the answer the question requires. Hence, 0 = 16 - 1/x2 , giving values of x = + 0.25 and -0.25.
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