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

1 Answer
Dec 16, 2016

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!