For the function f(x)=4x + 3sin(x), find all intervals where the function is increasing, decreasing, and its critical points.

So I know that to find where its increasing and decreasing, I have to find the derivative and set it equal to 0. So far I have 3cos(x)+4. Now this is where I have trouble solving for x. I forgot how to do this haha. Would it be cos(x)=-4/3 and then x=arccos(-4/3)?

Question

For the function f(x)=4x + 3sin(x), find all intervals where the function is increasing, decreasing, and its critical points. 

So I know that to find where its increasing and decreasing, I have to find the derivative and set it equal to 0. So far I have 3cos(x)+4. Now this is where I have trouble solving for x. I forgot how to do this haha. Would it be cos(x)=-4/3 and then x=arccos(-4/3)?

ganeshie8 · Answer

yes, also keep in mind cosx swings between [-1, 1]

anonymous · Answer

Whenever I input arccos(-4/3), I'm getting domain error. What am I doing wrong?

ganeshie8 · Answer

error is expected cuz, cosx never goes beyond -1 or +1

ganeshie8 · Answer

-4/3 = 1.somthing 
soo....

ganeshie8 · Answer

-1.somethig*