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How do you find the average rate of change of #f(x)= 2/x^2# over the interval [1, 5]?

Answer 1

Ezekiel Alexander

The average rate of change is #bar C = 13/25#

The incremental ratio computed over the entire interval is the average rate of change, which is:

#bar C = (f(b)-f(a))/(b-a)#

Here:

#bar C = ( [ 2/5^2 ] + [ 2/1^2 ])/(5-1)=1/4(2/25+2)=13/25#

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Answer 2

Emily Ammerman

To find the average rate of change of ( f(x) = \frac{2}{x^2} ) over the interval [1, 5], you first need to calculate the value of the function at the endpoints of the interval. Then, you subtract the value of the function at the starting point from the value of the function at the ending point. Finally, you divide this difference by the length of the interval. So, the average rate of change of ( f(x) = \frac{2}{x^2} ) over the interval [1, 5] is ( \frac{\frac{2}{5^2} - \frac{2}{1^2}}{5 - 1} ). This simplifies to ( \frac{2}{25} - \frac{2}{1} \div 4 ). Calculating this, the average rate of change is ( -\frac{3}{5} ).

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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.