How do you find the average rate of change for the function #f(x) = 4x^3 - 8x^2 - 3# on the indicated intervals [-5,2]?

Answer 1

The average rate of change for the function #f(x) = 4x^3 - 8x^2 - 3# on the interval #[-5,2]# is #(Deltaf)/(Deltax) = 100#

The average rate of change of function #f# on interval #[a,b]# is:
#(Deltaf)/(Deltax) = (f(b)-f(a))/(b-a)#
In this case, we have #a=-5#, abd #b = 2#, so we get:
#(Deltaf)/(Deltax) = (f(2)-f(-5))/(2-(-5))#
# = (-3-(-703))/7#
# = 700/7 = 100#
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Answer 2

To find the average rate of change of the function ( f(x) = 4x^3 - 8x^2 - 3 ) on the interval ([-5, 2]):

  1. Evaluate ( f(x) ) at the endpoints of the interval: ( f(-5) ) and ( f(2) ).
  2. Calculate the difference in function values: ( f(2) - f(-5) ).
  3. Divide the difference in function values by the difference in ( x )-values (interval length): ( \frac{{f(2) - f(-5)}}{{2 - (-5)}} ).
  4. Simplify the expression 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.

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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