Maximum and Minimum Values (Trig)

In summary, the problem involves finding the 4 critical points of the function f(x,y) = 5ycos(9x) closest to the point (0,0). The partial derivatives fx and fy are calculated and used to find the critical points, which are given by the x-values (1/18)pi(3), (1/18)pi(-1), (1/18)pi(-3), and (1/18)pi(1).
  • #1
Chas3down
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Homework Statement


Find the 4 critical points f(x,y) = 5ycos(9x) closest to (0,0)

Homework Equations

The Attempt at a Solution



fx = -45ysin(9x)
fy = 5cos(9x)
fxx = -45*9ycos(9x)
fyy = 0
fxy = -45sin(9x)

y=0
x=pi/18

(0,pi/18) (0,pi/18 + pi/2) (0,pi/18 - pi/2) (0,pi/18 + 3pi/2) Was not correct.

(All 4 points need to be correct for me to check it )
 
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  • #2
Usually the x-coordinate comes first and y second in the notation.
And check the spacing of the solutions in x, it is not pi/2.
 
  • #3
mfb said:
Usually the x-coordinate comes first and y second in the notation.
And check the spacing of the solutions in x, it is not pi/2.

Oops, I tried it correctly first but then swapped to see if that helped with anything, i put it back in x/y

But, i redid the problem and got..
y=0, x = (1/18)pi(4n-1)
y=0, x = (1/18)pi(4n+1)

Not sure how to translate that to the 4 closest points? Tried this but didn't work..

((1/18)pi(4-1),0), ((1/18)pi(0-1),0), ((1/18)pi(4+1),0), ((1/18)pi(0+1),0)
 
  • #4
I don't know how powerful the automatic (?) system to check the points is. I would not try to feed it with calculations like that. Maybe it needs decimal numbers, maybe something like 3/18 pi is okay (but where is the point in things like "4-1"?
((1/18)pi(4+1),0) is not among the 4 closest points.
 
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Likes Chas3down
  • #5
mfb said:
I don't know how powerful the automatic (?) system to check the points is. I would not try to feed it with calculations like that. Maybe it needs decimal numbers, maybe something like 3/18 pi is okay (but where is the point in things like "4-1"?
((1/18)pi(4+1),0) is not among the 4 closest points.

Ah, thanks a bunch!
Solution:
((1/18)pi(3),0), ((1/18)pi(-1),0), ((1/18)pi(-3),0), ((1/18)pi(1),0)
 

Related to Maximum and Minimum Values (Trig)

1. What is the definition of a maximum value in trigonometry?

A maximum value in trigonometry is the highest point on a graph of a trigonometric function. It represents the maximum possible value that the function can take within a given interval.

2. How can I find the maximum value of a trigonometric function?

To find the maximum value of a trigonometric function, you can use calculus techniques such as finding the derivative and setting it equal to zero. You can also use a graphing calculator to visually determine the highest point on the graph.

3. Can a trigonometric function have more than one maximum value?

Yes, a trigonometric function can have multiple maximum values within a given interval. This occurs when the function has multiple peaks or high points on its graph.

4. What is a minimum value in trigonometry?

A minimum value in trigonometry is the lowest point on a graph of a trigonometric function. It represents the minimum possible value that the function can take within a given interval.

5. How can I determine the minimum value of a trigonometric function?

To determine the minimum value of a trigonometric function, you can use calculus techniques such as finding the derivative and setting it equal to zero. You can also use a graphing calculator to visually determine the lowest point on the graph.

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