Applications of Derivatives Test

Result

Applications of Derivatives Test - 27

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Weekly Quiz Competition

Question 1
4 / -1

If f(x) = sin x/e^x in [0, π], then f(x)

A

B

C

D

Solution
Question 2
4 / -1

The function f defined by f(x) = 4x⁴ - 2x + 1 in increasing for

A
x < 1

B
x > 0

C
x < 1/2

D
x > 1/2

Solution
Question 3
4 / -1

A function f is defined by f(x) = 2 + (x - 1)^2/3 in [0, 2]. Which of the following is not correct?

A
f is not derivable in (0, 2)

B
f is continuous in [0, 2]

C
f(0) = f(2)

D
Rolle's theorem is correct in [0, 2]

Solution
Question 4
4 / -1

The function f(x) = cot^-1 x + x increases in the interval

A
(1, ∞)

B
(-1, ∞)

C
(-∞, ∞)

D
(0, ∞)

Solution
Question 5
4 / -1

In the interval (-3, 3) the function

A
increasing

B
decreasing

C
neither increasing nor decreasing

D
partly increasing and partly decreasing

Solution
Question 6
4 / -1

A
Both A and R are correct and R is the correct reason for A

B
Both A and R are correct are correct and R is not the correct reason for A

C
A is correct but r is incorrect

D
A is incorrect but R is correct

Solution
Question 7
4 / -1

A

B
(-∞,∞) - {2}

C
(-∞,∞) - {3}

D
(-∞,∞) - {2,3}

Solution
Question 8
4 / -1

A particle moves in a straight line so that it covered a distance at^{3 + bt + 5 metre in t seconds. If its acceleration after 4 seconds is 48 m/s², then a is equal to}

A
1

B
2

C
3

D
4

Solution
Question 9
4 / -1

The approximate value of f(5.001), where
f(x) = x³ - 7 x² + 15 is

A
-34.995

B
-33.995

C
-33.335

D
-35.995

Solution
Question 10
4 / -1

If there is an error of ± 0.04 cm in the measurement of the diameter of a sphere, then the approximate percentage error in its volume, when the radius is 10 cm, is

A
± 1.2

B
± 0.06

C
± 0.006

D
± 0.6

Solution