Find the x that maximizes the function f defined as ffxx122x

Find the x that maximizes the function f defined as ffx)-x1/2-2x

Solution

Answer:- f(x)=x^1/2-2x

For maximization:- df(x)/dx =0

d/dx(x^1/2-2x)=0

0.5x^-0.5-2 =0

x^-0.5= 5

5x^0.5=1

X=0.04

Answer:- f(x)=4x-2x²-110

For maximization:- df(x)/dx =0

d/dx(4x-2x²-110)=0

4-4x=0

X=1

Answer:- K³-2I²

d/dK(K³-2I²) = 3K²

Answer:- Y=AkI

d/dA(AkI)=KI

Answer:- Y= Ak^0.4I^0.6

d/dI(Ak^0.4I^0.6) =0.6Ak^0.4I^-0.4

Answer:- 100x+2y=1

100x-2y=1

Adding both the equation,

200x=2

X=0.01

100*0.01+2Y=1

Y=0

2x+3z=5-------1

3x+2z=5-----------2

Multiplying eq.1 with 3 and eq. 2 with 2 and then subtracting

6x+9z=15

-6x-4z=-10

5z=5

Z=1

Putting z=1 in eq. 1

X=(5-3)/2 =1