Applications of Derivatives Test

Result

Applications of Derivatives Test - 63

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
4 / -1

A

B

C

D

Solution
Question 2
4 / -1

It is a continuous function f defined on the real line R, assume positive and negative values in R then the equation f(x) = 0 has root in R. For example, if it is known that a continuous function f on R is positive at some point and its minimum value is negative then the equation f(x) = 0 has a root in R. Consider f(x) = ke^x – x for all real x where k is a real constant.
The line y = x meets y = ke^x for k ≤ 0 at

A
No point

B
One point

C
Two points

D
More than two points

Solution
Question 3
4 / -1

It is a continuous function f defined on the real line R, assume positive and negative values in R then the equation f(x) = 0 has root in R. For example, if it is known that a continuous function f on R is positive at some point and its minimum value is negative then the equation f(x) = 0 has a root in R. Consider f(x) = ke^x – x for all real x where k is a real constant.
The positive value of k for which ke^x – x = 0 has only one root is

A

B
1

C
e

D

Solution
Question 4
4 / -1

It is a continuous function f defined on the real line R, assume positive and negative values in R then the equation f(x) = 0 has root in R. For example, if it is known that a continuous function f on R is positive at some point and its minimum value is negative then the equation f(x) = 0 has a root in R. Consider f(x) = ke^x – x for all real x where k is a real constant.

A

B

C

D

Solution
Question 5
4 / -1

A
g is increasing on (1, ∞)

B
g is decreasing on (1, ∞)

C
g is increasing on (1, 2) and decreasing on (2, ∞)

D
g is decreasing on (1, 2) and increasing on (2, ∞)

Solution
Question 6
4 / -1

A
Both P and Q are true

B
P is true and Q is false

C
P is false and Q is true

D
Both P and Q are false

Solution
Question 7
4 / -1

This section contains some integer type questions. The answers to each of the questions is a single – digit integer, ranging from 0 to 9
The minimum value of the sum of real numbers a^–5, a^–4, 3a^–3,1,a⁸ and a¹⁰, where a > 0 is

A
5

B
6

C
8

D
7

Solution
Question 8
4 / -1

This section contains some integer type questions. The answers to each of the questions is a single – digit integer, ranging from 0 to 9

A
2

B
3

C
1

D
8

Solution
Question 9
4 / -1

This section contains some integer type questions. The answers to each of the questions is a single – digit integer, ranging from 0 to 9

A
2

B
3

C
4

D
1

Solution
Question 10
4 / -1

This section contains some integer type questions. The answers to each of the questions is a single – digit integer, ranging from 0 to 9
Let p(x) be real polynomial of least degree which has a local maximum at x = 1 and a local minimum at x = 3. If p(1) = 6 and p(3) = 2, then p’(0) is

A
9

B
5

C
13

D
4

Solution