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