Applications of Derivatives Test

Result

Applications of Derivatives Test - 26

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Weekly Quiz Competition

Question 1
4 / -1

A
even and strictly increasing in (0, ∞)

B
odd and is strictly decreasing in (- ∞, ∞)

C
odd and is strictly decreasing in (-∞, ∞)

D
neither even nor odd but is strictly increasing in (-∞, ∞)

Solution
Question 2
4 / -1

How many real solutions does the equation x⁷ + 14x⁵ + 16x³ + 30x - 560 = 0 have ?

A
5

B
7

C
1

D
3

Solution
Question 3
4 / -1

A
an increasing

B
a decreasing

C
an even

D
None of these

Solution
Question 4
4 / -1

If the function f(x) ax³ + bx² + 11x - 6 satisfies the condition of Rolle's theorem in [1, 3] and

A
-1, 6

B
-2, 1

C
1, -6

D
-1, 1/2

Solution
Question 5
4 / -1

Select the correct statement from (a), (b), (c) and (d). The function f(x) = xe^{1 - x}

A
strictly increases in the interval (1/2, 2)

B
increases in the interval (0, ∞)

C
decreases in the interval (0, 2)

D
strictly decreases in the interval (1,∞)

Solution
Question 6
4 / -1

Rolle's theorem is not applicable to the function f (x) = |x| for -2 ≤ x ≤ 2 because

A
f is continuous for -2 ≤ x ≤ 2

B
f is not derivable for x = 0

C
f(-2) = f(2)

D
f is not a constant function

Solution
Question 7
4 / -1

If f(x) = 3x⁴ + 4x³ - 12x² + 12, then f(x) is

A
increasing in (-∞ - 2) and in (0, 1)

B
increasing in (-2, 0) and (1, ∞)

C
decreasing in (-2, 0) and (0, 1)

D
decreasing in (-∞, -2) in (1, ∞)

Solution
Question 8
4 / -1

The function f(x) = 2x³ + 13x² - 12x + 1 decreases in the interval

A
(2, 3)

B
(1, 2)

C
(-2, -1)

D
(-3, -2)

Solution
Question 9
4 / -1

A value of c for which the conclusion of mean value theorem holds for the function f(x) = log_e x on the interval [1, 3] is

A
2 log₃ e

B
1/2 log_e 3

C
log₃ e

D
log_e 3

Solution
Question 10
4 / -1

The value of b for which function f(x) = sin x - bx + c is decreasing in the interval (-∞, ∞) is given by

A
b < 1

B
b ≥ 1

C
b > 1

D
b ≤ 1

Solution