The pdf contains multiple type questions on the topic APPLICATIONS OF DERIVATIVES.
The pdf contains the most important questions and covers all the topics in depth.
Answers have been also given on the last page.
The sign of 𝑓 ′ (𝑥) changes from positive to negative as x increases through x = a then
2 A) 𝑥 = 𝑎 is a point of local minimum B) 𝑥 = 𝑎 is a point of local maximum
C) 𝑥 = 𝑎 is a point of inflection D) None of these
The sign of 𝑓 ′ (𝑥) changes from negative to positive as x increases through x = a then
3 A) 𝑥 = 𝑎 is a point of local minimum B) 𝑥 = 𝑎 is a point of local maximum
C) 𝑥 = 𝑎 is a point of inflection D) None of these
Maximum value of sin x. cos x is
4 1 1
A) 2 B) 4 C) √2 D) 2√2
Maximum slope of the curve y = −𝑥 3 +3𝑥 2 + 9𝑥 − 27 is
5
A) 0 B) 12 C) 16 D) 32
The function 𝑓(𝑥) = 2𝑥 3 −3𝑥 2 − 12𝑥 + 4, has
6 A) two points of local maximum B) two points of local minimum
C) one maxima and one minimum D) neither maximum nor minimum
5𝜋
At x = , f(x) = 2 sin 3x + 3 cos 3x has a
6
7
A) maxima B) minima C) zero D) neither a maximum nor a minimum
ZIET, BHUBANESWAR Page 1
, f(x) = 𝑥 𝑥 has a stationery point at x =
8
1
A) 𝑒 B) 𝑒 C) 1 D) √𝑒
1−𝑥+𝑥 2
For all real values of x, the minimum value of 1+𝑥+𝑥 2
9 1
A) 0 B) 1 C) 3 D) 3
1 𝑥
The maximum value of (𝑥) is
10 1
1 𝑒
A) 𝑒 B) 𝑒 𝑒 C) 𝑒 𝑒 D) (𝑒)
The maximum and minimum values of 𝑓(𝑥) = 𝑥 + sin 2𝑥 in the interval [ 0, 2𝜋 ] are
11
A) 2𝜋 , 0 B) 0, 2𝜋 C) 0, 0 D) None of these
Let f(x) be a function such that 𝑓 ′ (𝑎) ≠ 0. Then at x = a, f(x)
A) cannot have a maximum B) cannot have a minimum
12
C) have neither a maximum nor a minimum D) None of these
Two numbers whose sum is 24 and whose product is as large as possible. Then the two numbers are
13 A) 16, 8 B) 12 , 12 C) 10, 14 D) 11, 13
2 −𝑥
The critical point(s) of f(x) = 𝑥 𝑒 is/are
14
A) 0 B) 2 C) both A & 𝐵 D) None of these
The function f(x) = 𝑥 2 𝑒 −𝑥 has
15
A) local minimum at x = 0 only B) local maximum at x = 2 only C) both
A and B D) None of these
The function 𝑓(𝑥) is said to be strictly decreasing if
(A) 𝑓′(𝑥)> 0
(B) 𝑓′(𝑥) ≥ 0
(C) 𝑓′(𝑥)< 0
(D) 𝑓′(𝑥) ≤ 0
16
The function given by f (x) = 3x + 17 is
(A) strictly increasing on R.
(B)strictly decreasing on R.
(C)Neither increasing nor decreasing on R.
17
ZIET, BHUBANESWAR Page 2
, (D)decreasing on R.
The function given by f (x) = e2x is
(A) strictly increasing on R.
(B)strictly decreasing on R.
(C)Neither increasing nor decreasing on R.
(D)decreasing on R.
18
The intervals in which the function f given by f(x) = 2x2 – 3x is strictly increasing is
3
(A)(4 , ∞)
3
(B)[4 , ∞)
3
(C)(−∞, 4)
3
(D)(−∞, 4]
19
The logarithmic function f(x) = log x is
(A) strictly decreasing on (0, ∞).
(B) strictly increasing on (0, ∞).
(C) increasing on (0, ∞).
(D) Neither increasing nor decreasing on (0, ∞).
20
𝜋
Which of the following functions is strictly decreasing on (0, 2 )?
(A) cos x
(B) cos 2x
(C) cos 3x
(D) tan x
21
The interval in which y = x2 e–x is increasing is
(A) (– ∞, ∞)
(B) (– 2, 0)
(C) (2, ∞)
(D) (0, 2)
22
𝜋
The function f given by f(x) = log sin x is strictly increasing on(0, 2 )
𝜋
(A)is increasing on(0, 2 )
𝜋
(B)is decreasing on(0, 2 )
𝜋
(C)is strictly decreasing on(0, 2 )
23
ZIET, BHUBANESWAR Page 3
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