Critical Points, Inflection Points, Increasing/Decreasing Functions

1). f(x)=ln(2x^2+1)

Use derivatives to find the x-values of any critical points and inflection points exactly.

critical points (enter as a comma-separated list): x= 0

inflection points (enter as a comma-separated list): x= ???

The critical point is zero, but I'm not sure what the inflection point is. I thought it was also zero, but that is incorrect.

2). For the function f(x)=2x^3−6x+7, find all intervals where the function is increasing.

Similarly, find all intervals where the function is decreasing.

I know you take the derivative, which is 6x^2-6. I believe then you set it equal to zero and then test points. However, I'm not getting the correct answer.

3). For the function f(x)=8x+5sin(x). The derivative is 5cosx+8. Find all intervals where the function is increasing.

Similarly, find all intervals where the function is decreasing.

Please help!