Minima Definition and 110 Threads

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)...