Page 58 - Mathematics Class - XII

Viva-Voce

1. What is the use of maxima/minima of function in real life?
Ans. The concepts of maxima/minima are useful in problems of daily life such as making of packages of
maximum capacity at minimum cost.

2. Explain point of local maxima.
Ans. It is the point where f ′(x) = 0 and sign of derivative changes from positive to negative.
3. Explain point of local minima.

Ans. It is the point where f ′(x) = 0 and sign of derivative changes from negative to positive.
4. Define extreme point.

Ans. Function f is said to have an extreme value in I if there exists a point c in I such that f (c) is either a
maximum value or a minimum value of f in I. The number f (c), in this case, is called an extreme value
of f in I and the point c is called an extreme point.

5. What is point of inflection?
Ans. A point where the graph of a function is continuous and where the concavity changes is a point
of inflection.

MCQs

1. If x is a real number then the minimum value of x – 8x + 17 is
2
a) 0 b) 1 c) –1 d) 2

2. The function given by f (x) = 2x – 3x – 12x + 4
3
2
a) a maxima and a minima b) are two local minima points
c) neither maximum nor minimum d) are two local maxima points

5
3. The value of f (x) = 2 sin 3x + 3 cos 3x at x is
6
a) 0 b) Minimum
c) Maximum d) Neither maximum nor minimum

4. The maximum and minimum value of the function 2x – 15x + 36 x + 6
3
2
a) 34, 33 b) 33, 34 c) –33, –34 d) None of these
5. The maximum value of function f (x) = sin x.cos x will be

a) 1 b) 2 c) 1 d) 1
2 4 2
Answers: 1. b) 1 2. a) a maxima and a minima 3. c) Maximum

4. a) 34, 33 5. a) 1
2
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