Application of Derivatives Test

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Application of Derivatives Test - 2

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Weekly Quiz Competition

Question 1
1 / -0

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

A
(-∞, 0)

B
(0, ∞)

C
(-∞, ∞)

D
none of these
Question 2
1 / -0

The function f (x) = x² , for all real x, is

A
decreasing

B
increasing

C
neither decreasing nor increasing

D
none of these
Question 3
1 / -0

A car starts from a point P at time t = 0 seconds and stops at the point Q . The distance x, in metres covered by it, in t seconds is given by x = t² (2 - t/3) The distance between P and Q is

A
4 m

B
32/3 m

C
32 m

D
none of these
Question 4
1 / -0

The angle between the curves y² = x and x² = y at (1, 1) is

A
tan^-1 (4/3)

B
tan^-1 (3/4)

C
90^o

D
45^o
Question 5
1 / -0

Slope of tangent to the curve x = a sin³ t, y = b cos³ t at t = π/2 is

A
not defined

B
1

C
-1

D
0
Question 6
1 / -0

A manufacturer can sell x items at a price of Rs (5- x/100) each. The cost price of x items is Rs ((x/5) +500). The number of items, the manufacturer should sell to earn maximum profit is

A
500

B
100

C
420

D
240
Question 7
1 / -0

The function f (x) = x² - 4 x + 6 is

A
strictly decreasing on [2, ∞]

B
strictly increasing on (- ∞, 2]

C
strictly increasing on R

D
strictly increasing on [2, ∞)
Question 8
1 / -0

The total revenue Rs R received from the sale of x units of a product is given by R (x) = 3 x2 + 36 x + 5 The marginal revenue when x = 5 is (marginal revenue is the rate of change of total revenue w.r.t. number of items sold at an instant)

A
66

B
Rs 66

C
69

D
none of these
Question 9
1 / -0

On R, the function f (x) = 7 x - 3 is

A
strict decreasing

B
decreasing

C
increasing

D
strict increasing
Question 10
1 / -0

The function f(x) = log {x³ + √(x⁶ + 1)} is

A
even and increasing

B
even and increasing

C
odd and decreasing

D
odd and increasing

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Re-Attempt Weekly Quiz Competition

Application of Derivatives Test - 2

Result

Application of Derivatives Test - 2

Score

-

Rank

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SHARING IS CARING

Question 1

(-∞, 0)

(0, ∞)

(-∞, ∞)

none of these

Question 2

decreasing

increasing

neither decreasing nor increasing

none of these

Question 3

4 m

32/3 m

32 m

none of these

Question 4

tan-1 (4/3)

tan-1 (3/4)

90o

45o

Question 5

not defined

1

-1

0

Question 6

500

100

420

240

Question 7

strictly decreasing on [2, ∞]

strictly increasing on (- ∞, 2]

strictly increasing on R

strictly increasing on [2, ∞)

Question 8

66

Rs 66

69

none of these

Question 9

strict decreasing

decreasing

increasing

strict increasing

Question 10

even and increasing

even and increasing

odd and decreasing

odd and increasing

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tan^-1 (4/3)

tan^-1 (3/4)

90^o

45^o