SOLUTION: 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<=2pie? Where? Thanks!

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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<=2pie? Where?
Thanks!
Found 2 solutions by ikleyn, solver91311:
Answer by ikleyn(52875)   (Show Source): You can put this solution on YOUR website!
.
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!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

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.




Figure. Plot y = 3x + 6*sin(x)


Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


ikleyn's answer is spot on, but this graph restricted to the indicated domain and the unit circle illustration may prove helpful.





And, by the way, "pie" is dessert, "pi" is the ratio of a circle's circumference to its diameter. Just sayin'

John

My calculator said it, I believe it, that settles it

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