Question 1019971
.
Hi, this a question from calculus 1.

It says: Does the graph of the function y=3x+6sin(x)have any horizontal tangents in the interval 0 <=x<=2*pi? Where?

Thanks!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
Take the derivative and equate it to zero:

3 + 6*cos(x) = 0.

Try to solve it for x in the given interval.

Use the plot below for inspiration.
</pre>

<TABLE> 
  <TR>
  <TD> 

{{{graph( 330, 330, -2.5, 8.5, -2.5, 12.5,
          3x + 6*sin(x)
)}}}


<B>Figure</B>. Plot y = 3x + 6*sin(x)

  </TD>
  </TR>
</TABLE>