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Find the minimum value of the function f(x) = x^2 – 2x – 7 to the nearest hundredth. a) -6.00 b) -5.99 c) -4.00 d) -3.99

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The minimum value of a function can be found using the derivative of the function. For differentiable functions like ours, differentiating the function and setting the result to zero gives us the x-coordinate of the minimum value we are searching for.

The given quadratic function f(x) = x^2 - 2x - 7 has a derivative f'(x) of 2x - 2. Setting 2x - 2 = 0 and solving for x gives us x = 1.

Next, we need to substitute x = 1 into the original function to find the minimum value. So, substituting x = 1 into the function, we get:

f(x) = (1^2 - 2*1 - 7) = -8.

Therefore, the minimum value of the function f(x) = x^2 - 2x - 7 is -8. If we wish to express this value to the nearest hundredth, since there are no decimals, we can write it as -8.00. So, the correct answer is not in the provided options a, b, c, or d. The minimum value is -8.00.

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