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

1 Answer
Dec 16, 2016

Answer:

#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!