Page 64 - Mathematics Class - XII

Viva-Voce

1. What is the volume of cuboid?
Ans. Volume of cuboid = length × breadth × height

2. What is the use of this given activity in real life?
Ans. This activity is useful in making packages of maximum volume with minimum cost.
3. Explain the second property of maxima and minima.

Ans. Maxima and minima occur alternately, i.e., between two minima there is one maxima and vice-versa.
4. Given a function f (x) if x belongs to p is a point obtained from the equation f ′(p) = 0 and f ″(p) > 0, then
what can you say about p and f (p)?

Ans. In this case, p is point of minima and f (p) has taken as minimum value of f (x).
5. What is the volume of cuboid, if its length = breadth = height?
Ans. If in a cuboid, length = breadth = height = x (say)

then it will become a cube of side x and volume = x .
3

MCQs

1. Maximum value of the function, f (x) = x3 + 2x2 +1 is

a) 2.185 b) –2.185 c) –1 d) 1

2. Maximum value of the function, f (x) = –6 x2 – 3 x – 2 is

a) − 8 b) 13 c) − 13 d) 8
13 8 8 13
3. Minimum value of the function, f (x) = 3x 2– 2 x + 8 is, if x is real.

a) 23 b) 23 c) 25 d) 29
2 3 3 2
4. Minimum value of function, f (x) = (x – 2) (x – 9) is

a) 49 b) 0 c) 11 d) − 49
4 4 4
5. If, f (x) = | x + 1| + | x + 10 |, then find the minimum value of f (x) is

a) 10 b) 1 c) 9 d) 21

Answers: 1. a) 2.185 2. c) − 13 3. b) 23 4. d) − 49 5. c) 9
8 3 4

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