# How to find instantaneous rate of change for #g(x) = x^2 − x + 4# at x=-7?

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To find the instantaneous rate of change for ( g(x) = x^2 - x + 4 ) at ( x = -7 ), you would first find the derivative of the function ( g(x) ) with respect to ( x ). Then, you would evaluate the derivative at ( x = -7 ) to find the instantaneous rate of change.

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

Evaluating ( g'(x) ) at ( x = -7 ), we get:

[ g'(-7) = 2(-7) - 1 = -14 - 1 = -15 ]

So, the instantaneous rate of change of ( g(x) ) at ( x = -7 ) is ( -15 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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