Applications of Derivatives Test

Result

Applications of Derivatives Test - 23

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
4 / -1

A
3

B
1/3

C
2

D
1/2

Solution
Question 2
4 / -1

On the interval [0, 1], the function x²⁵ (1 - x)⁷⁵ takes its maximum value at the point

A
0

B
1/4

C
1/2

D
1/3

Solution
Question 3
4 / -1

A
a local maximum

B
a local minimum

C
no local extremum

D
no local maximum

Solution
Question 4
4 / -1

A
x = - 2

B
x= 0

C
x = 1

D
x = 2

Solution
Question 5
4 / -1

Angle between the tangents to the curve y = x² - 5x + 6 at the points (2, 0) and (3,0) is

A
π/2

B
π/6

C
π/4

D
π/3

Solution
Question 6
4 / -1

If the curve y = 2x³ + ax² + bx + c passes through the origin and the tangent drawn to it at x = - 1 and x = 2 are parallel to the X - axis, then the values of a, b and c are respectively

A
12, -3 and 0

B
-3, -12 and 0

C
-3, 12 and 0

D
3, -12 and 0

Solution
Question 7
4 / -1

The tangent and the normal drawn to the curve y = x² - x + 4 at P(1, 4) cut the X - axis at A and B, respectively. If the length on the subtangent drawn to the curve at P is equal to the length of the subnormal, then the area of the ∆PAB(in sq units) is

A
4

B
32

C
8

D
16

Solution
Question 8
4 / -1

If the line ax + by + c = 0 is a normal to the curve xy = 1, then

A
a > 0, b > 0

B
a > 0, b < 0

C
a < 0, b < 0

D
Data is insufficient

Solution
Question 9
4 / -1

The maximum value of x^1/x is

A
1/e^e

B
e

C
e^1/e

D
1/e

Solution
Question 10
4 / -1

The set {x³ - 12x : -3 ≤ x ≤ 3} is equal to

A
{x : -16 ≤ x < 16}

B
{x : -12 ≤ x < 12}

C
{x : -9 ≤ x < 9}

D
{x : 0 ≤ x < 10}

Solution