Find the maximum and minimum values, if any, of the following functions given by (i) f (x) = (2x – 1)^2 + 3 (ii) f(x) = 9x ^2 + 12x + 2

(i) Given:  

Since  for all  R

Adding 3 both sides,     

Therefore, the minimum value of  is 3 when , i.e., 

This function does not have a maximum value.

(ii) Given:  

 

 

= 

        ……….(i)

Since  for all  R

Subtracting 2 from both sides, 

 

Therefore, minimum value of  is  and is obtained when , i.e., 

And this function does not have a maximum value.