Given Y = -2X2 + 20X - 20 1)Find the optimal value of X 2)Is this a maximum or minimum point? Explain

Economics Feb 20, 2021

Given Y = -2X² + 20X - 20

1)Find the optimal value of X

2)Is this a maximum or minimum point? Explain.

Expert Solution

1. At optimal value of X, ∂Y/∂X = 0

Y = - 2 X² + 20 X - 20

∂Y/∂X = - 4 X + 20

-4 X + 20 = 0

4 X = 20

X = 20/ 4

= 5

2. To find whether the optimal point is a maximum or a minimum point, we find the second derivative. If the second derivative is negative, then it is a maximum point. If the second derivative is positive, then it is a minimum point.

∂Y/∂X = - 4 X + 20

∂²Y/∂X² = - 4

This therefore means that it is a minimum point.

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