Question

The maximum possible value of y = min (1/2 – 3x2
/4, 5x2
/4) for the range 0 < x < 1 is
(a) 1/3
(b) 1/2
(c) 5/27
(d) 5/16

Answer 1

option d is right answer

Answer 2

Answer:

5/16

Step-by-step explanation:

The maximum possible value of y = min (1/2 – 3x2

/4, 5x2

/4) for the range 0 < x < 1 is

(a) 1/3

(b) 1/2

(c) 5/27

(d) 5/16

y = min(  1/2 - 3x²/4  ,  5x²/4)

to find maximum possible value

1/2 - 3x²/4  = 5x²/4

multiplying by 4 both sides

2 - 3x² = 5x²

=> 2 = 8x²

=> x² = 2/8

=> x² = 1/4

=> x = ±1/2  

x = 1/2  ( as 0 < x < 1)

maximum possible value of y when x = 1/2

y = 5x²/4 = 5(1/2)²/4 = 5/16

option D is correct

maximum possible value of y = min(  1/2 - 3x²/4  ,  5x²/4)  is 5/16