Question

Suppose i have a function:

A*(3-x)+B*A(sqrt(x^2+4)).

Find the x-value of the critical point of this cost function, where A,B illustrate the cost.

This point will be a function of U

Answer 1

@wio

Answer 2

the function illustrates the cost function, but how do you find the critical point of it when you have A and B to worry about...i tried differentitiating and i got\[C=-A+BAx(x^2+4)\]

Answer 3

when C' sorry

Answer 4

where C is the cost function

Answer 5

so i let C'=0 and i get
\[-A+BAx(x^2+4)=0\]

Answer 6

\[Bx(x^2+4)=1\]

Answer 7

Are you sure you differentiated correctly?

Answer 8

o i forgot the -1/2 aye

Answer 9

\[C'=-A+\frac{ BAx }{ \sqrt(x^2+4) }\]

Answer 10

so when C'=0
\[Bx=\sqrt(x^2+4)\]

Answer 11

Yeah, technically you could solve further.

Answer 12

\[B^2x^2=x^2+4\]

Answer 13

\[x^2(B^2-1)-4=0\]

Answer 14

Ah, difference of squares.

Answer 15

\[(x-\sqrt(B-1))(x+\sqrt(B-1))=0\]

Answer 16

\(x>0\)

Answer 17

so x=sqrt(B-1)?

Answer 18

ive tried this answer but it says its incorrect

Answer 19

o wait i see my mistake

Answer 20

yea i got it!