Applications of Derivatives Test

Result

Applications of Derivatives Test - 38

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
4 / -1

Let C be the curve y³ − 3xy + 2 = 0. If H is the set of points on the curve C where the tangent is horizontal and V is the set of points where the tangent is vertical, then H and V are respectively given by :

A
{(0, 0)}, {(0, 1)}

B
φ, {(1, 1)}

C
{(1, 1)}, {(0, 0)}

D
None of these

Solution
Question 2
4 / -1

Tangent at a point P₁, (other tan (0, 0)) on the curve y = x³ meets the curve again at P₂. The tangent at P2 meets the curve at P3 and so on. Then the abscissa of P₁, P₂,P₃, …. are in :

A
A.P.

B
G.P.

C
H.P

D
None of these

Solution
Question 3
4 / -1

If the normal to the curve x^2/3 + y^2/3 = a^2/3 makes an angle φ with the x−axis, then its equation is :

A
x sin φ + y cos φ = a

B
y cos φ − x sin φ = a cos 2φ

C
x cos φ + y sin φ = a sin 2 φ

D
none of these

Solution
Question 4
4 / -1

A
both f(x) and g(x) are increasing functions

B
both f(x) and g(x) are decreasing functions

C
f(x) is increasing function and g(x) is an increasing function

D
None of these

Solution
Question 5
4 / -1

A
0

B
1

C
2

D
infinite

Solution
Question 6
4 / -1

A
does not exist because f is unbounded

B
is not attained even though f is bounded

C
is equal to 1

D
is equal to − 1

Solution
Question 7
4 / -1

A
0, 4

B
1, 3

C
0, 2

D
2, 4

Solution
Question 8
4 / -1

If f’(x)= g(x) (x − a)², where g(a) ≠ 0 and g is continuous at x = a, then : f\'(x)

A
f is increasing in the nbd. of a if g(a) > 0 and f is decreasing in the nbd. of a if g(a) < 0

B
f is increasing in the nbd. of a if g(a) < 0

C
f is decreasing in the nbd. of a if g(a) > 0

D
f is increasing in the nbd. of a if g(a) < 0 and f is decreasing in the nbd. of a if g(a) > 0

Solution
Question 9
4 / -1

The function f(x) defined by f(x) = (x + 2) e^−x is :

A
decreasing for all x

B
decreasing in (−∞, −1) and increasing in (−1, ∞)

C
increasing for all x

D
decreasing in (−1, ∞) and increasing in (− ∞, −1)

Solution
Question 10
4 / -1

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

A
0

B

C

D

Solution