Question

Find the critical numbers of the function f(x)=12cos(x)⋅6sin ²(x).

A) x=0
B) x= 2/π
​C) x=π
D) x= 2/3π
​

Answer 1

The critical numbers of the function f(x)=12cos(x)\u00b76sin \u00b2(x) are found by differentiating the function and setting the derivative equal to zero. Solving for x gives the critical numbers x = 0, \u03c0, \u03c0/3, and 5\u03c0/3.

Step-by-step explanation:

The student is asking to find the critical numbers of the function f(x)=12cos(x)\u00b76sin \u00b2(x). Critical numbers are values of x at which the first derivative f'(x) is either 0 or undefined.

To find these, we need to differentiate the given function and solve for the values of x where the derivative is 0.Let's differentiate the function: