Test: Application Of Derivatives - 2

Question 1

The function f (x) = x²– 2 x is increasing in the interval

Accepted Answer

x &#10878; 1

Answer

x &#10878; &#8722;1

Answer

x &#8800; &#8722;1

Answer

x &#8800; 1

Question 2

The function f (x) = a x + b is strict increasing for all x ∈ R iff

Accepted Answer

a &#62; 0

Answer

a &#60; 0

Answer

a = 0

Answer

none of these.

Question 3

Tangents to the curve x²+y² = 2at the points (1, 1) and (– 1, 1)

Accepted Answer

at right angles

Answer

parallel

Answer

intersecting but not at right angles

Answer

none of these

Question 4

If x be real, the minimum value of x²−8x+17 is

Accepted Answer

1

Answer

&#8211; 1

Answer

2

Answer

0

Question 5

If a differentiable function f (x) has a relative minimum at x = 0, then the function y = f (x) + a x + b has a relative minimum at x = 0 for

Accepted Answer

all b if a = 0

Answer

all a &#62; 0.

Answer

all b &#62; 0

Answer

all a and all b

Question 6

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

Accepted Answer

neither decreasing nor increasing

Answer

Decreasing

Answer

Increasing

Answer

none of these

Question 7

The function f (x) = a x + b is strict increasing for all x ∈ R if

Accepted Answer

a > 0

Answer

a = 0

Answer

a < 0

Answer

none of these.

Question 8

Equation of the tangent to the curve at the point (a, b) is

Accepted Answer

Answer

Answer

Answer

none of these

Question 9

a log | x | + bx² + x has its extreme values at x = – 1 and x = 2, then

Accepted Answer

a = 2, b = <img src="https://cn.edurev.in/ApplicationImages/Temp/59_ffe64128-e128-46bd-b157-2a0f26b1be80_lg.PNG" />

Answer

Answer

Answer

a = 2, b = – 1

Question 10

Let f (x) be differentiable in (0, 4) and f (2) = f (3) and S = {c : 2 < c < 3, f’ (c) = 0} then

Accepted Answer

S has atleast one point

Answer

S has exactly one point

Answer

S = { }

Answer

none of these

Question 11

The function f (x) = m x + c where m, c are constants, is a strict decreasing function for all x ∈ R if

Accepted Answer

m &#60; 0

Answer

m &#62; 0

Answer

m &#10878; 0

Answer

m = 0

Question 12

The function f (x) = x²−2x is strict decreasing in the interval

Accepted Answer

(−∞, 1]

Answer

R

Answer

[1,&infin;)

Answer

none of these

Question 13

The points on the curve 4 y = |x²−4| at which tangents are parallel to x – axis, are

Accepted Answer

(0, 1) only

Answer

(4, 3) and (– 4, – 3)

Answer

(2, 0) and (– 2, 0)

Answer

none of these

Question 14

The maximum value of

Accepted Answer

1/e

Answer

0

Answer

&ndash; e

Answer

none of these

Question 15

Every continuous function is

Accepted Answer

not necessory differentiable

Answer

not decreasing

Answer

decreasing

Answer

differentiable.

Question 16

The function f(x) = tan⁻¹x is

Accepted Answer

strict increasing

Answer

neither increasing nor decreasing

Answer

differentiable nowhere.

Answer

strict decreasing

Question 17

For the curve x = t²−1,y = t²−t tangent is parallel to X – axis where

Accepted Answer

t =1/2

Answer

t = <img src="https://cn.edurev.in/ApplicationImages/Temp/59_ac091845-d419-4fd7-8698-9162f6dbf262_lg.PNG" />

Answer

t = 0

Answer

t = - <img src="https://cn.edurev.in/ApplicationImages/Temp/59_ac091845-d419-4fd7-8698-9162f6dbf262_lg.PNG" />

Question 18

The slope of the normal to the curvex = a (cos θ + θ sin θ),y = a (sin θ – θ cos θ) at any point ‘θ’ is

Accepted Answer

– cot θ.

Answer

tan &theta;

Answer

&ndash; tan &theta;

Answer

cot &theta;

Question 19

Accepted Answer

Answer

Answer

has a maximum value 2

Answer

has a minimum value 0

Question 20

Rolle’s Theorem is not applicable to the function f(x) = | x | for −2⩽x⩽2 because

Accepted Answer

f (x) is not derivable for x = 0

Answer

f (– 2) = f (2)

Answer

f (x) is continuous for −2⩽x⩽2 because

Answer

none of these

Question 21

Let f (x) = x³−6x²+9x+8, then f (x) is decreasing in

Accepted Answer

[1, 3]

Answer

(−∞,1) ∪ (3,∞)

Answer

[3,&infin;]

Answer

(&minus;&infin;,1)

Question 22

The equation of the normal to the curve y = sinx at (0, 0) is

Accepted Answer

x + y = 0

Answer

y = 0

Answer

x = 0

Answer

x – y = 0

Question 23

The curve y = x^1/5 has at (0, 0)

Accepted Answer

a vertical tangent

Answer

oblique tangent

Answer

no tangent.

Answer

a horizontal tangent

Question 24

Accepted Answer

local minima at x = 2 and a local maxima at x = – 2

Answer

a local maxima at x =2 and a local minima at x = – 2

Answer

absolute minima at x = 2 and absolute maxima at x = – 2.

Answer

absolute maxima at x = 2 and absolute minima at x = – 2

Question 25

Accepted Answer

sin x < x < tan x

Answer

tan x < x < sin x

Answer

x< sin x < tan x

Answer

none of these

Application Of Derivatives - 2 - Free MCQ Practice Test with solutions,

MCQ Practice Test & Solutions: Test: Application Of Derivatives - 2 (25 Questions)

The function f (x) = x²– 2 x is increasing in the interval

The function f (x) = a x + b is strict increasing for all x ∈ R iff

Tangents to the curve x²+y² = 2at the points (1, 1) and (– 1, 1)

If x be real, the minimum value of x²−8x+17 is

If a differentiable function f (x) has a relative minimum at x = 0, then the function y = f (x) + a x + b has a relative minimum at x = 0 for

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

The function f (x) = a x + b is strict increasing for all x ∈ R if

Equation of the tangent to the curve at the point (a, b) is

a log | x | + bx² + x has its extreme values at x = – 1 and x = 2, then

Let f (x) be differentiable in (0, 4) and f (2) = f (3) and S = {c : 2 < c < 3, f’ (c) = 0} then

The function f (x) = m x + c where m, c are constants, is a strict decreasing function for all x ∈ R if

The function f (x) = x²−2x is strict decreasing in the interval

The points on the curve 4 y = |x²−4| at which tangents are parallel to x – axis, are

The maximum value of

Every continuous function is

The function f(x) = tan⁻¹x is

For the curve x = t²−1,y = t²−t tangent is parallel to X – axis where

The slope of the normal to the curvex = a (cos θ + θ sin θ),y = a (sin θ – θ cos θ) at any point ‘θ’ is

Rolle’s Theorem is not applicable to the function f(x) = | x | for −2⩽x⩽2 because

Let f (x) = x³−6x²+9x+8, then f (x) is decreasing in

The equation of the normal to the curve y = sinx at (0, 0) is

The curve y = x^1/5 has at (0, 0)

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Application Of Derivatives - 2 - Free MCQ Practice Test with solutions,

MCQ Practice Test & Solutions: Test: Application Of Derivatives - 2 (25 Questions)

The function f (x) = x2 – 2 x is increasing in the interval

The function f (x) = a x + b is strict increasing for all x ∈ R iff

Tangents to the curve x2+y2 = 2at the points (1, 1) and (– 1, 1)

If x be real, the minimum value of x2−8x+17 is

If a differentiable function f (x) has a relative minimum at x = 0, then the function y = f (x) + a x + b has a relative minimum at x = 0 for

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

The function f (x) = a x + b is strict increasing for all x ∈ R if

Equation of the tangent to the curve at the point (a, b) is

a log | x | + bx2 + x has its extreme values at x = – 1 and x = 2, then

Let f (x) be differentiable in (0, 4) and f (2) = f (3) and S = {c : 2 < c < 3, f’ (c) = 0} then

The function f (x) = m x + c where m, c are constants, is a strict decreasing function for all x ∈ R if

The function f (x) = x2−2x is strict decreasing in the interval

The points on the curve 4 y = |x2−4| at which tangents are parallel to x – axis, are

The maximum value of

Every continuous function is

The function f(x) = tan−1x is

For the curve x = t2−1,y = t2−t tangent is parallel to X – axis where

The slope of the normal to the curvex = a (cos θ + θ sin θ),y = a (sin θ – θ cos θ) at any point ‘θ’ is

Rolle’s Theorem is not applicable to the function f(x) = | x | for −2⩽x⩽2 because

Let f (x) = x3−6x2+9x+8, then f (x) is decreasing in

The equation of the normal to the curve y = sinx at (0, 0) is

The curve y = x1/5 has at (0, 0)

Mathematics (Maths) for JEE Main & Advanced

Mathematics (Maths) for JEE Main & Advanced

Top Courses for JEE

About this JEE Practice Test

Explore more JEE Study Resources

The function f (x) = x²– 2 x is increasing in the interval

Tangents to the curve x²+y² = 2at the points (1, 1) and (– 1, 1)

If x be real, the minimum value of x²−8x+17 is

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

a log | x | + bx² + x has its extreme values at x = – 1 and x = 2, then

The function f (x) = x²−2x is strict decreasing in the interval

The points on the curve 4 y = |x²−4| at which tangents are parallel to x – axis, are

The function f(x) = tan⁻¹x is

For the curve x = t²−1,y = t²−t tangent is parallel to X – axis where

Let f (x) = x³−6x²+9x+8, then f (x) is decreasing in

The curve y = x^1/5 has at (0, 0)