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

Answer 1

Elijah Abram

#-15#

#"the instantaneous rate of change is the value of"# #g'(-7)#

#g'(x)=2x-1#

#g'(-7)=-14-1=-15#

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Answer 2

Elijah Abram

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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Answer from HIX Tutor

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.