Question

Find the maximum value of the function Y = min (x2 - 4,4 - x2) for x, where -3 <
X< 3.​

Answer 1

Step-by-step explanation:

Given y=x

3

−3x

2

+6

Differentiating y w.r.t. x,

dx

dy

=3x

2

−6x

Putting dy/dx=0, we get the values at which the function is maximum or minimum. So

3x

2

−6x=0

⇒x(3x−6)=0⇒x=0,+2

To distinguish the values of x as the point of maximum or minimum, we need second derivative of the function.

∴

dx

2

d

2

y

=6x−6; Now (

dx

2

d

2

y

)

x=0

=−6<0.

So x=0 is a point of maximum.

Similarly, (

dx

2

d

2

y

)

x=+2

=6>0

So x=+2 is a point of minimum.

Hence, the maximum value of y is 0

3

−3×0+6=6 and the minimum value of y is (2)

3

−3(2)

2

+6=2.