Question

What is the maximun of f(x)=3cosx+2sinx ?

Whithout using derivatives

Answer 1

how about limits? lol

Answer 2

@seidi.yamauti are you aware of what the graphs of cosx and sinx look like?

Answer 3

@abayomi12 he said without using derivatives.

Answer 4

ok

Answer 5

I'd simplify this first:
f(x) = 2 * sin(x) * cos(x)
f(x) = sin(2x)

Answer 6

max value of acosx+bsinx is sqrt(a^2+b^2) and min is -sqrt(a^2+b^2)
thus here max value is sqrt(3^2+2^2)

Answer 7

\[a\cos x+b\sin x=\sqrt{a^2+b^2} (\frac{a}{\sqrt{a^2+b^2}}\cos x+\frac{b}{\sqrt{a^2+b^2}}\sin x)\] using the fact that\[(\frac{a}{\sqrt{a^2+b^2}})^2+(\frac{b}{\sqrt{a^2+b^2}})^2=1\] u can prove\[\sqrt{a^2+b^2} (\frac{a}{\sqrt{a^2+b^2}}\cos x+\frac{b}{\sqrt{a^2+b^2}}\sin x)=\sqrt{a^2+b^2} \sin(x+\alpha)\]or\[\sqrt{a^2+b^2} (\frac{a}{\sqrt{a^2+b^2}}\cos x+\frac{b}{\sqrt{a^2+b^2}}\sin x)=\sqrt{a^2+b^2} \cos(x+\beta)\]

Answer 8

cool.. B|

Answer 9

in other words, use the identity
sin(x+y) = sin(x)cos(y)+cos(x)sin(y)

Answer 10

maximum = sqrt(3^2 + 2^2) = sqrt(13)

Answer 11

अगर आप चाहें तो वोल्फ्रम का उपयोग कर सकते हैं.

Answer 12

बात समझ आई?

Answer 13

@mukushla आप तो मास्टर हो, मास्टर!

Answer 14

man this is hindi !

Answer 15

ye cid walay yahan kya kar rahay hain :P

Answer 16

@sami-21 Kya chal raha hai?

Answer 17

@sami-21 chutti pe hain hum sab

Answer 18

humari police

Answer 19

btw just to let you know guys irreverent answers are considered as SPAM .

Answer 20

lol

Answer 21

You can use a special trig identity: Acos(x) + Bsin(x) = Ccos(x-y), where C=\sqrt{A^2=B^2) and y = arctan(B/A). Hence
\[f(x)=3\cos x + 2\sin x = \sqrt{13}\cos\left(x-arctan\tfrac{2}{3}\right)\approx\sqrt{13}\cos\left(x-.588\right)\]
But in any case, the maximum for cos is 1, so the maximum for f(x) is the square root of 13.

Answer 22

also \(a\sin(x)+b\cos(x)=\sqrt{a^2+b^2}\sin(x+\theta)\) for suitable \(\theta\)
as i recall you can get this from "addition angle" formula

Answer 23

@satellite73, how are you inserting equations without linebreaks? $ signs don't seems to work here (as they would in LaTeX).

Answer 24

use \( instead of \[

Answer 25

Thank you.

Answer 26

you are right, $ does not work here
turns out \( is an alternative in latex

if you need to see any code, right click and you can see it. it is good method for copying and pasting as well, so you don't have to rewrite the latex every time