Question

How can you find the absolute maximum value of the function f(x)=sin(x)?

A) By taking the derivative and setting it equal to zero.
B) By finding critical points and evaluating f(x) at those points.
C) Since sin(x) has no critical points, the absolute maximum occurs at =0x=0.
D) By finding the local maximum points and comparing their values.

Answer 1

To find the absolute maximum value of the function f(x) = sin(x), we evaluate f(x) at its critical points. However, since sin(x) has no critical points, we know that its absolute maximum occurs when f(x) = sin(x) is equal to 1.

The Correct Option is; C) Since sin(x) has no critical points, the absolute maximum occurs at x = 0.

Step-by-step explanation:

The absolute maximum value of the function f(x) = sin(x) can be found by evaluating f(x) at its critical points and comparing their values. Since the derivative of sin(x) is cos(x), we can find the critical points by setting cos(x) equal to zero. However, since cos(x) is never equal to zero, there are no critical points for the function f(x) = sin(x).

Since sin(x) is a periodic function that oscillates between -1 and +1, the maximum value of f(x) = sin(x) is 1. This occurs when x is at any multiple of π/2. Therefore, the absolute maximum value of f(x) = sin(x) is 1.