Question

(b) Find maximum and minimum values of :

y = (x – 3)3 (x + 1)2​

Answer 1

Answer:

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.