Applications of Derivatives Test

Result

Applications of Derivatives Test - 21

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
4 / -1

A
1

B
2/e

C
e

D
1/e

Solution
Question 2
4 / -1

A
x = 0

B
x = 1

C
x = 4

D
x = 3

Solution
Question 3
4 / -1

If m and M respectively denote the minimum and maximum of f(x) = (x - 1)² + 3 for x ϵ [-3, 1], then the ordered pair (m, M) is equal to

A
(-3, 9)

B
(3, 19)

C
(-19, 3)

D
(-19, -3)

Solution
Question 4
4 / -1

The length of the subtangent at (2, 2) to the curve x⁵ = 2y⁴ is

A
5/2

B
8/5

C
2/5

D
5/8

Solution
Question 5
4 / -1

The equation of the normal to the curve y⁴ = ax³ at (a, a) is

A
x + 2y = 3a

B
3x - 4y + a = 0

C
4x + 3y = 7a

D
4x - 3y = 0

Solution
Question 6
4 / -1

If y = 4x - 5 is a tangent to the curve y² = px³ + q at (2, 3), then

A
p = 2, q = -7

B
p = - 2, q = 7

C
p = -2, q = -7

D
p = 2, q = 7

Solution
Question 7
4 / -1

A
a local maxima at x = 1 and a local minima at x = - 1

B
a local minima at x = 1 and a local maxima at x = - 1

C
absolute maxima at x = 1 and absolute minima at x = -1

D
absolute minima at x = 1 and absolute maxima at x = -1

Solution
Question 8
4 / -1

The normal to a curve at P(x, y) meets the X - axis at G. If the distance of G from the origin is twice the abscissa of P, then the curve is a

A
ellipse

B
parabolla

C
circle

D
hyperbola

Solution
Question 9
4 / -1

The minimum value of 2x + 3y, when xy = 6 is

A
9

B
12

C
8

D
6

Solution
Question 10
4 / -1

If the function f(x) = x² e^-2x, x > 0. Then, the maximum value of f(x) is

A
1/e

B
1/2e

C
1/e²

D
4/e⁴

Solution