Question

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

Answer 1

Please help!

Answer 2

Draw out the graph :)

Answer 3

i have to use derivatives though!

Answer 4

The derivative must be 0.
So derivate the function and search for the values of x where the derivate equals 0

Answer 5

horizontal tangent means y=c line now find the derivative and make slope=0

Answer 6

i found the values to be 2pi/3 and 4pi/3, but the answer in my book puts it as an expression: (2n+1)pi +/- pi/3

Answer 7

Yeah sinx = -1/2 so use general solution y =sinx
x = sin-1(y) + 2kπ and x = −sin-1(y) + (2k+1)π,