In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema), or on the entire domain (the global or absolute extrema). Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions.
As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum.
Homework Statement
A hypothetical star S has a planet P that moves in an elliptical orbit with period T . The minimum distance of P from S is d and the maximum distance is 1.7d.
(i) find the maxima and minima of the magnitude of the acceleration of P, in terms of d and T .
Homework...
Optimization, Minima, new question:Sheet Alluminum
Homework Statement
A box with a square base and no top must haave a volume of 10000 cm^3. If the smallest dimension in any direction is 5 cm, then determine the dimensions of the box that minimize the amount of material used.
Homework...
I have a function that is not giving me critical points for where their appears to be a maximum.
from plot their seems to be a cp at approximately x=y=5
However, these are the cp's:
cpx =
-0.2618
-1.3090
1.8326
2.8798
-2.8798
-1.8326
1.3090
0.2618cpy =
-0.2618...
How would we find the maximum surface area of a cylinder inscribed in a sphere of radius R. This problem is given in my textbook . I know concept of maxima and minima will be apllicable here but i can,t start and make the expression of surface area in a suitable manner. Anybody having answers
Two speakers are drive by a common oscillator at 800 Hz and face each other a distance of 1.25 m. Locate the points along a line joining the two speakers where relative minima would be expected (v =343m/s speed of sound)
How would I do this? I think I would just take part of the wavelength...
Hi I am stuck on this ques. although i have solved and got the ans but i am still facing a problem.
Find the shortest distance of the point (0,c) from the parabola y=x^2 where 0<= c <= 5
i got the ans right that is
(c-0.25)^0.5
but i have not been able to understand the use of the 0<= c <= 5...
Greetings, can you guys please help me with my assignment??
I am supposed to find and classify all critical points of the function f(x,y) = (sin x)(cos y)
Now I took the first partials with repsect to x and y and they are (cos x)(cos y) = 0 and (-sin x)(sin y) = 0, respectively.
Now I...
Find the coordinates of a stationary point on the curve y= \frac{16x^3 + 4x^2 + 1}{2x^2} And determine the nature of this points.
How I find the coordinates? I know the second part.
Hello all
You are planning to make an open box from a 30- by 42 inch piece of sheet metal by cutting congruent squares from the corners and folding up the sides. You want the box to have the largest possible volume.
(a) What size square should you cut from each corner? (gice side length of...
Hello all
Given y = -x^4 + 18x^2 + 11 how would you find the intervals where the function is increasing and decreasing? Would you have to find f'(x) and find critical points?
Thanks
Hello all
I have a few questions on applied maxima and minima
1. A company gives you 675 sq. ft of cardboard to construct a rectangular carton with the largest volume. If the carton is to have a square base and an open top, what dimensions would you use?
My Thought Process:
Volume =...
I have u(x,t)=-2xt-x^2 find maximum in region {-2 ≤ x ≤ 2 , 0 ≤ t ≤ 1}
I believe to find the critical point first I have to take the partial derivative with respect to x and t and equate to zero.
Thus
Ux=-2t-2x = 0
Ut=-2x = 0
Thus the only critcal point I find is x=0, t=0.
But the...
Calculus maxima and minima word question...can't understand :(
A rectangular field is going to be enclosed and divided into two separate rectangular areas (not equal either). Find the minimum fencing required if the total area of the field is 1200m^2
(See the picture attached right now)...