Page 95 - Mathematics Class - XI

Viva-Voce

1. Does derivative at a point show normal to the point?
Ans. No. Derivative at a point shows slope of tangent to the point.

2. Find the derivative of x + y = 1.
Ans. 1 1
x y 1
2
2
1 1
1 1 dy
x 2 y 2 0
2 2 dx
dy y
dx x
3. Find the derivative of x .
n
Ans. Derivative of x = nx n – 1 .
n
4. Find slope of tangent at a point on the curve y = x.
dy
Ans. Slope of tangent = = 1 = tan 45°.
dx
5. Find the derivative of xy = 8 at (5, 5).
dy
Ans. = –1 at (5, 5).
dx

MCQs

1. If y x 5 , then what will be the value of dy at x = 1?
x 9 dx
a) 2 b) 3 c) −7 d) None of these
32
1 dy
2. If y x , the what will be the value of at x = 1?
x dx
a) 0 b) 2 c) –2 d) 3

3. If f (x) = |sin x|, where x 3 then what will be the value of f

3
2
1
a) 1 b) − 3 c) − d) 0
2 5 2
4. If f (x) = 1 – x + x – x + ............ – x + x then f '(1) is equal to
99
100
3
2
a) –50 b) 100 c) 50 d) –100
5. If f (x) = x + x + ......... + x + 1, then what will be the value of f '(1)
100
99
a) 5050 b) 5049 c) 5051 d) 5052
1
Answers: 1. c) −7 2. a) 0 3. c) − 4. c) 50 5. a) 5050
32 2
93