Question

For what values of x does the graph of f have a horizontal tangent `f(x)=x+2sinx`?

Answer 1

`x= (2pi)/3, (4pi)/3`, in the interval `0 ≤ x ≤2pi`

Explanation:

Start by differentiating.

`f'(x) = 1 + 2cosx`

The derivative represents the instantaneous rate of change of the function. A horizontal tangent will have a `0` slope. Therefore, we set the derivative to `0` and solve.

`0 = 1 + 2cosx`

`-1/2 = cosx`

`x = (2pi)/3 and (4pi)/3`

Hopefully this helps!