Divide 15 into two parts such that the square of one multiplied by the eighth of the other is maximum.find the two parts?

Question

738 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-27T12:09:24

# 10, and, 5.#

Let the parts be #x and y," hence, "x+y=15.............(1).#

By what has been said, these #x and y# should be such that, the

value of #x^2*y/8# may become maximum.

Because of #(1), x^2/8(15-x),# is to be maximised, which is a fun.

of #x#, so, let us write, #f(x)=x^2/8(15-x)=1/8(15x^2-x^3).#

As is known, for #f_max, f'(x)=0, and, f''(x) < 0.#

# f'(x)=0 :. 1/8(15*2x-3x^2)=0 :. x=0, or, x=10.#

Also, #f'(x)=1/8(30x-3x^2) :. f''(x)=1/8(30-3*2x)=6/8(5-x).#

#rArr f''(0)=6/8*5 >0, and, f''(10)=6/8(5-10) <0.#

Hence, #x=10# yields #f_max.#

Therefore, the reqd. parts are, #10, and, 5.#

Enjoy Maths.!

.

this, being a fun. of #x