Barungi Regan
Apr 9
find the absolute maximum or minimum of the function f(x)=2x+(8/x)+2 for x is not equal to 0 ?
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Apr 9
To find the absolute maximum or minimum of the function f(x) = 2x + (8/x) + 2, we first need to find the critical points of the function.
To find the critical points, we take the derivative of the function and set it equal to zero:
f'(x) = 2 - 8/x^2
Setting f'(x) equal to zero, we get:
2 - 8/x^2 = 0
8/x^2 = 2
x^2 = 4
x = ±2
So, the critical points are x = 2 and x = -2.
Next, we need to check the endpoints of the domain of the function, which is x is not equal to 0. Since x cannot equal 0, we do not have to consider it as an endpoint.
Now, we evaluate the function at the critical points and the endpoints:
f(2) = 2(2) + 8/2 + 2 = 4 + 4 + 2 = 10
f(-2) = 2(-2) + 8/-2 + 2 = -4 - 4 + 2 = -6
Therefore, the absolute maximum of the function is 10 at x = 2, and the absolute minimum is -6 at x = -2.
To find the critical points, we take the derivative of the function and set it equal to zero:
f'(x) = 2 - 8/x^2
Setting f'(x) equal to zero, we get:
2 - 8/x^2 = 0
8/x^2 = 2
x^2 = 4
x = ±2
So, the critical points are x = 2 and x = -2.
Next, we need to check the endpoints of the domain of the function, which is x is not equal to 0. Since x cannot equal 0, we do not have to consider it as an endpoint.
Now, we evaluate the function at the critical points and the endpoints:
f(2) = 2(2) + 8/2 + 2 = 4 + 4 + 2 = 10
f(-2) = 2(-2) + 8/-2 + 2 = -4 - 4 + 2 = -6
Therefore, the absolute maximum of the function is 10 at x = 2, and the absolute minimum is -6 at x = -2.
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