Find the x-coordinates where f ' (x)=0 for f(x)=2x+sin(4x) in the interval [0, pi]

The x-coordinate is \dfrac{\pi}{6}[/tex].

Step-by-step explanation:

We are given a function f(x) as:

Now on differentiating both side with respect to x we get that:

When

this means that

Hence, cosine function takes the negative value in second and third quadrant but we have to only find the value in the interval .

also we know that ----(1) (which lie in the second quadrant)

so on comparing our equation with equation (1) we obtain:

Hence, the x-coordinates where for is .