In column (I) y is given in terms of x and in column (II) its maximum or minimum value is given.
Column I | Column II |
(i) y = x2 – x3 maximum or minimum value of y between x = 0 to x = 1 | [A] |
(ii) y = x – x2 + 7 maximum value of y | [B] |
(iii) y = sin x + cos x maximum value of y is | [C] |
(iv) y = sin x – cos x maximum value of y is | [D] Zero |
[E] None |
Text Solution
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Ans.
(i) [C, D]
(ii) [B]
(iii) [A]
(iv) [A]
Sol. (i) y = x 2 – x 3 
= 2x – 3x
2 = 0
x = 0, 
= 2 – 6x
at π = 0, 
> = 0, y min = 0
at x = 
, 
< 0
y max. = 
– 
= 
(ii) y = x – x 2 + 7
= 1 – 2x = 0, x = 
= – 2
y max = 
+ 7 = 
(iii) y = sin + cos x
= cos x – sin x = 0
tan x = 1
x = 
y min = 
(iv) y = sin x – cos x
= cos x + sin x = 0
tan x = – 1, x = – 
= – sin θ + cos θ < 0
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