# What is the instantaneous rate of change for #g(x) = x^2 − x + 4# when x=-7?

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To find the instantaneous rate of change for (g(x) = x^2 - x + 4) when (x = -7), we need to find the derivative of the function and evaluate it at the given point.

The derivative of (g(x)) with respect to (x) is (g'(x) = 2x - 1).

Now, substitute (x = -7) into the derivative: [g'(-7) = 2(-7) - 1] [g'(-7) = -14 - 1] [g'(-7) = -15]

Therefore, the instantaneous rate of change for (g(x) = x^2 - x + 4) when (x = -7) is (-15).

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