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

Answer 1

Isaiah Allen

#-15#

Find #g'(-7)#.

Use the power rule: #d/dx(x^n)=nx^(n-1)#

#g'(x)=2x^(2-1)-1x^(1-1)+0(4x^(0-1))#

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

Again, find the instantaneous rate of change by computing #g'(-7)#.

#g'(-7)=2(-7)-1=-14-1=-15#

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Answer 2

Isaiah Allen

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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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.