maximum of...


by AlbertEinstein
Tags: maximum
AlbertEinstein
AlbertEinstein is offline
#1
Jun23-06, 11:58 PM
P: 113
The question is find the maximum value of the following function

f(x) = 3cos(4*pi*x-1.3) + 5cos(2*pi*x+0.5).
Phys.Org News Partner Mathematics news on Phys.org
Hyperbolic homogeneous polynomials, oh my!
Researchers help Boston Marathon organizers plan for 2014 race
'Math detective' analyzes odds for suspicious lottery wins
HallsofIvy
HallsofIvy is offline
#2
Jun24-06, 09:22 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,898
"The question"? Where, in your homework?

Looks pretty straight forward to me: differentiate and set the derivative equal to 0. Use the sin(a+b) formula to isolate [itex]sin(3\pi x)[/itex] and [itex]cos(3\pi x)[/itex].
AlbertEinstein
AlbertEinstein is offline
#3
Jun25-06, 02:06 AM
P: 113
Hey HallsofIvy,

Your suggestion was quite correct. However I dare say differentiating and equating to zero does not always help.
Here f (x) = 3cos (4*pi*x-1.3) + 5cos (2*pi*x+0.5)
Or, f (x) = - [12*pi*sin (4*pi*x-1.3) + 10*pi*sin (2*pi*x+0.5)]
Equating this to zero,
12*pi*sin (4*pi*x-1.3) + 10*pi*sin (2*pi*x+0.5)] = 0
Now if I use the sin (a+b) formula the equation gets rather complicated.

I shall be thankful to you if you could please show the full solution.
However the answer is 5.7811.

HallsofIvy
HallsofIvy is offline
#4
Jun25-06, 12:16 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,898

maximum of...


Yes, it gets complicated. Anything wrong with that? You'll also, by the way, need to use the double angle formulas to reduce [itex]4\pi x[/itex] to [itex]2\pi x[/itex]. After you done all that, you will have an equation of the form [itex]A sin(2\pi x)+ B cos(2\pi x)= 0[/itex] with rather complicated numbers for A and B. But they are only numbers! Write [itex]tan(2\pi x)= -B/A[/itex] and solve.


Register to reply

Related Discussions
maximum torque, maximum power Introductory Physics Homework 8
Maximum volume General Math 1
How to find the maximum velocity and maximum acceleration? Introductory Physics Homework 5
maximum temperature Classical Physics 2
local maximum and global maximum. Introductory Physics Homework 3