Cannot find horizontal tangent of the curve

Asked May 16 '15 at 20:45

Active May 16 '15 at 21:42

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Does the curve represented by the equation $y= \cos x + 5x$ have any horizontal tangent?

I calculated $y\prime=0$ and i got $\sin x=5$ which is false so what should i do ?

Here is what i did : $$ y = \cos x +5x,\\ y\prime=-\sin x +5 $$ I have $$ y\prime = 0 \implies -\sin x + 5 = 0\implies \sin x = 5 $$

edited May 16 '15 at 21:42

Chinny84

asked May 16 '15 at 20:45

Ali Zgheib

1

So no horizontal tangent exists – WW1 May 16 '15 at 20:48
1

the slope of $y = 5x + \cos x$ is between $4$ and $6.$ – abel May 16 '15 at 21:00
@abel how did u find him ? – Ali Zgheib May 16 '15 at 21:07
y'=0 gave you no solutions so there are no horizontal tangents @Ali Zgheib – randomgirl May 16 '15 at 21:09
$y'=-\sin(x)+5$..Recall $-1 \le -\sin(x) \le 1$. So $-1+5 \le y' \le 1+5$ – randomgirl May 16 '15 at 21:12

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