Applications of Derivatives Test

Result

Applications of Derivatives Test - 17

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Weekly Quiz Competition

Question 1
4 / -1

If x is real, then the minimum value of

A
3

B
1/3

C
1/2

D
2

Solution
Question 2
4 / -1

The condition that f(x) = ax³ + bx² + cx + d has no extreme value is

A
b² > 3ac

B
b² = 4ac

C
b² = 3ac

D
b² < 3ac

Solution
Question 3
4 / -1

Find the slope of the normal to the curve 4x³ - 3xy² + 6x² - 5xy - 8y² + 9x + 14 = 0 at the point (-2, 3)

A
∞

B
1

C
9/2

D
2/9

Solution
Question 4
4 / -1

Let f : [0,1] → R(the set of all real numbers) be a function. Suppose the function f is twice differentiable,
f(0) = f(1) = 0 and satisfies f ''(x) - 2f '(x) + f(x) ≥ e^x, x ϵ [0,1].
A line L : y = mx + 3 meets Y - axis at E(0, 3) the arc of the parabola y² = 16x, 0 ≤ y ≤ 6 at the point F(x_o , y_o). The tangent to the parabola at F(x₀, y_o) interest the Y - axis at G(0, y₁). The slope m of the line L is chosen such that the area of ∆EFG has a local maximum

A
A = 4, B = 1, C = 2, D = 3

B
A = 3, B = 4, C = 1, D = 2

C
A = 1, B = 3, C = 2, D = 4

D
A = 1, B = 3, C = 4, D = 2

Solution
Question 5
4 / -1

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. The lengths of the sides of the rectangular sheet are

A
24

B
32

C
45

D
60

Solution
Question 6
4 / -1

The function f(x) = 2|x| + |x + 2|-1||x - 2|x|| has a local minimum or a local maximum at

A
-2

B
-2/3

C
2

D
2/3

Solution
Question 7
4 / -1

The intercepts on X - axis made by tangents to the curve,

A
± 1

B
± 2

C
± 3

D
± 4

Solution
Question 8
4 / -1

The equation of the tangent to the curve y = e^|x| at the point, where the curve cuts the line x = 1 is

A
e(x + y) = 1

B
y = ex = 1

C
x + y = e

D
None of these

Solution
Question 9
4 / -1

If at each point of the curve y = x³ - ax² + x + 1 tangent is inclined at an acute angle with the positive direction of the X-axis, then

A
a ≤ √3

B
a > 0

C
- √3 ≤ a ≤ √3

D
None of these

Solution
Question 10
4 / -1

The difference between the greatest and the least value of the function

A

B

C

D
None of these

Solution