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the function y = a x 4 1 x has a minimum at the point ( 1 12 5 , f ( 1 12 5 ) ) . determine the value of a.

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Final answer:

To determine the value of a, we need to find the derivative of the function and set it equal to zero. The derivative of the function y = ax^4 + 1/x is 4ax^3 - 1/x^2. To find the minimum, we set the derivative equal to zero. Solving for a, we find that a = 0.5387.

Step-by-step explanation:

To determine the value of a, we need to find the derivative of the function and set it equal to zero. The derivative of the function y = ax^4 + 1/x is 4ax^3 - 1/x^2. To find the minimum, we set the derivative equal to zero:

4ax^3 - 1/x^2 = 0

Simplifying the equation, we get:

4ax^5 - 1 = 0

Substituting x = 1.125 into the equation, we can solve for a:

4a(1.125)^5 - 1 = 0

Solving for a, we find that a = 0.5387.

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