"How do you find the average rate of..." solved and explained

Efrain Watkins

Answered question

2022-04-14

How do you find the average rate of change of

f (x) = \cot x

over the interval

[\frac{π}{4}, 3 \frac{π}{4}]

Nico Buck

Beginner2022-04-15Added 9 answers

f (x) = \cot x

The average rate of change of a function from

x = \frac{π}{4}

x = \frac{3 π}{4} i s \frac{f (\frac{3 π}{4}) - f (\frac{π}{4})}{\frac{3 π}{4} - \frac{π}{4}}

f (\frac{3 π}{4}) = \cot (\frac{3 π}{4}) = - 1

and

f (\frac{π}{4}) = \cot (\frac{π}{4}) = 1

∴ \frac{f (\frac{3 π}{4}) - f (\frac{π}{4})}{\frac{3 π}{4} - \frac{π}{4}} = \frac{- 1 - 1}{\frac{3 π}{4} - \frac{π}{4}}

= - \frac{2}{\frac{π}{2}} = - \frac{4}{π} \approx - 1.27 (2 d p)

The average rate of change of f(x) is -1.27(2dp)

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