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What is the average rate of change of the function #f(x)=2x^2 -3x -1# on the interval [2, 2.1]?

Answer 1

William Abdalla

#5.2#

The average rate of change of the function #f(x)# on the interval #[a,b]# is:

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

This provides us with

#"average rate of change"=(f(2.1)-f(2))/(2.1-2)#

For this function, #f(2)=1# and #f(2.1)=1.52#.

#"average rate of change"=(1.52-1)/(0.1)=0.52/0.1=5.2#

Addendum:

Halfway through the interval, the derivative (rate of change) of the function should be roughly equal to the average rate of change on this interval.

The derivative of the function is

#f'(x)=4x-3#

Halfway through the interval is at #x=2.05#, and the value of the derivative is

#f'(2.05)=5.2#

They are identical in this instance.

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Answer 2

Scarlett Allison

The average rate of change of the function (f(x) = 2x^2 - 3x - 1) on the interval ([2, 2.1]) is approximately (0.9).

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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.