The Difference Between The Greatest And Least Values Of The Function

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Question

The difference between the greatest and least values of the function

easy

Solution

Correct option is

9/4

The given function is periodic, with period 2π. So the difference between the greatest and least values of the function is the difference these values on the interval [0, 2π]. We have

Hence x = 0, 2π/3, π and 2π are the critical points. Also, f (0) = 1 + 1/2 – 1/3 = 7/6, f (2π/3) = –13/12, f (π) = –1/6 and f (2π) = 7/6. Hence the greatest value is 7/6 and the least value is – 13/12. Thus

the difference is