Answer true or false. f(x) = sin 4x cos 4x on has an absolute maximum at .

Question

Answer true or false. f(x) = sin 4x cos 4x on  has an absolute maximum at  .

Quizplus · Accepted Answer

To find the absolute maximum of a function, we need to check the endpoints of the interval and any critical points. However, this function does not have any critical points as its derivative simplifies to 0. Therefore, we only need to check the endpoints of the interval [0,pi/8]. When x=0, f(x)=0 and when x=pi/8, f(x)=sin(4pi/8)cos(4pi/8)=0. Thus, the absolute maximum value of the function is 0 and it is achieved at both endpoints.

Answer True or False