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what is the average rate of change of y = cos (2x) on the interval [0, π2]?

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The average rate of change of the function y = cos(2x) over the interval (0, π/2) is [tex] \frac{-4}{\pi}[/tex]

The average rate of change over a given interval is defined thus :

  • [tex] R = \frac{f(b) - f(a)}{b - a}[/tex]

  • Where a and b are the interval values

At a = 0 :

  • f(0) = cos(2(0)) = Cos 0 = 1

At b = π/2 :

  • f(π/2) = cos(2(π/2)) = Cos π = - 1

Hence,

[tex] \frac{f(b) - f(a)}{b - a} = \frac{-1-1)}{\frac{\pi}{2} - 0} = \frac{-2}{\frac{\pi}{2}} = \frac{-4}{\pi} [/tex]

Therefore, the average rate of change over the interval is [tex] \frac{-4}{\pi}[/tex]

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