Question

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

Answer 1

The function f(x)=sin(x) has a maximum value of +1 at x = π/2 and a minimum value of -1 at x = 3π/2 on the interval [0,2π).

Step-by-step explanation:

To find the x-values where the function f(x) = sin(x) has maximum or minimum values on the interval [0,2π), we look at the properties of the sine function. The sine function has a maximum value of +1 and a minimum value of -1. Since sine is periodic with a period of 2π radians, we know it reaches these values regularly throughout its cycle.

A maximum value of +1 occurs at x = π/2 and every 2π radians thereafter within the given interval. For a minimum value of -1, this occurs at x = 3π/2 within the interval [0,2π). Therefore, the function has a maximum at x = π/2 and a minimum at x = 3π/2 on the interval [0,2π)