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Let f(x) = cos(x). Determine the x-value(s) where the function has a maximum or minimum value on [0,2π).

User Joey Adams
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Final answer:

The function f(x) = cos(x) reaches its maximum value of 1 at x=0 and its minimum value of -1 at x=π within the interval [0,2π).

Step-by-step explanation:

The student has asked to determine the x-value(s) where the function f(x) = cos(x) has a maximum or minimum value on the interval [0,2π). Since the cosine function oscillates between -1 and 1, we know that the maximum value of cosine is 1 and occurs at an x-value that is a multiple of 2π. Similarly, the minimum value of cosine is -1 and occurs at an x-value that is an odd multiple of π.

On the interval [0,2π), the maximum value occurs at x=0 and the minimum value occurs at x=π. There is no maximum between π and 2π since cos(x) starts decreasing after x=0 and reaches its minimum at x=π, and then starts increasing again towards 1, but not achieving the maximum within this interval.

User NagyI
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