Question

Determine the Extreme values of the function f(x)=2 sin 4x + 3 XE[0, pi] I need help finding the x values for which their max/min using first derivitave

Answer 1

screw the derivative do it in your head
the largest sine can be is one
the largest 2 times sine can be is 2 and the largest two times sine plus 3 can be is 5

Answer 2

repeat for "smallest

smallest sine can be is minus one
smallest two times sine can be is minus two
the smallest two times sine plus 3 can be is one

Answer 3

yea, but im taking calculus, and my teacher expects to do the calculus way

Answer 4

So, what is the derivative?

Answer 5

tell your teacher that using derivatives in this case imparts no information
the derivative of sine is cosine
if you know about cosine, you know about sine
you are chasing your tail

Answer 6

As a side note, finding the critical points of the derivative is just as difficult as finding the minimum and maximum of the actual function here, since we know sin has max and min at 1 and 01.

Answer 7

then the derivative of cosine is minus sine
the derivative of minus sine is ....
you get the idea
it is stupid, a stupid waste of time going around in circles, saying you know about sine because you know about cosine and vice versa
tell your math teacher (gently) that you are too smart for such nonsense and he/she should be as well

Answer 8

the derivative of this function is 8 cos 4x,

Answer 9

so it is
set it equal to zero and solve for \(x\)

Answer 10

once i do that i ge 45/2, and then i dont know what to do after that, i get confused

Answer 11

\[8\cos(4x)=0\\
\cos(4x)=0\\
4x=\frac{\pi}{2}\\
x=\frac{\pi}{8}\]

Answer 12

you cannot use degrees in the context of calculus
the trig functions are functions of numbers, not angles measured in degrees
forget degrees

Answer 13

btw you might as well have set
\[2\sin(4x)=2\\
\sin(4x)=1\\
4x=\frac{\pi}{2}\\
x=\frac{\pi}{8}\]same thing exactly

Answer 14

ah i c makes sense now, thanks man

Answer 15

Ummm, what about \(5\pi/8\)?

Answer 16

I think \(3\pi/8\) is also a critical point.

Answer 17

And also \(7\pi/8\).

Answer 18

how did u get those?

Answer 19

Basically, \(x\in [0,\pi] \implies 4x\in[0,4\pi]\)

Answer 20

Then I got \(4x=\pi/2, \quad 4x=3\pi/2, \quad 4x=5\pi/2, \quad4x= 7\pi/2\).

Answer 21

The fact that \(4\pi\) is 2 full rotations and there are 2 answers per rotation means there had to be more than one answer.

Answer 22

Finally, \(0\) and \(2\pi\) are technically critical points simply for being on the boundaries.

Answer 23

whoops, I mean \(0\) and \(\pi\).

Answer 24

I do not get how you got \[3\pi/2\] and so on. im kind of confused on that part

Answer 25

ooh wait ive been doing it wrong lol, i was doing 270/ 360 instead of doing 270/180 to get i into rads lol