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How do you find the average rate of change of #f(x) = 4x^3 - 8x^2 - 3# from -5 to 2?

Answer 1

Luke Alvarez

#100#

The average rate of change of a function on the interval #a# to #b# is

#"average rate of change"=(f(a)-f(b))/(a-b)#

This provides us with

#"average rate of change"=(f(-5)-f(2))/(-5-2)#

The function values are located separately:

#f(-5)=4(-5)^3-8(-5)^2-3=-703#

#f(2)=4(2)^3-8(2)^2-3=-3#

Thus,

#"average rate of change"=(-703-(-3))/(-7)=(-700)/(-7)=100#

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Answer 2

Paisley Johnson

To find the average rate of change of ( f(x) = 4x^3 - 8x^2 - 3 ) from ( x = -5 ) to ( x = 2 ), calculate the difference in the function values at the endpoints of the interval and divide it by the difference in the independent variable values. In this case, the average rate of change can be found using the formula:

[ \text{Average rate of change} = \frac{f(2) - f(-5)}{2 - (-5)} ]

Substitute the values of ( f(x) ) at ( x = 2 ) and ( x = -5 ) into the formula, then perform the calculation to find the average rate of change.

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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.