# Find the smallest positive x-value where f(x)=x+4sin(2x) has a horizontal tangent line?

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must be in exact value.

thanks!

must be in exact value.

thanks!

##### 1 Answer

#### Explanation:

First, we have to understand what it means to have a horizontal tangent line.

We know that the slope of the tangent line to a function is determined by the derivative of the function. If a line is horizontal, its slope is zero.

So, we need to find the smallest value of

#f(x)=x+4sin(2x)#

The derivative of

In this case, the derivative of

#f'(x)=1+8cos(2x)#

We need to find when the derivative equals

#0=1+8cos(2x)#

Rearranging,

#cos(2x)=-1/8#

That is,

#2x=cos^-1(-1/8)#

The range of the

Thus:

#x=1/2cos^-1(-1/8)#

You said you wanted an exact value, so I'll leave it like this.