Let f x = 1 1 1 3 - x 5 - 3 x 2 3 x 3 - 1 2 x 2 - 1 3 x 5 - 1 7 x 8 - 1 . Then, the equation f x = 0 has

exactly one real root in 0, 1 and no other real root

Let fx be a differentiable function in the interval 02 then the value of 02fxdx

MEDIUM

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Proficiency in 'dy/dx as a Rate Measurer & Tangents, Normals' Exercise 1>Q 3

If

f (x)

be a fourth differentiable function such that

f (2 x^{2} - 1) = 2 x f (x), \forall x \in R

, then

f^{i v} (0)

(where

f^{i v} (0)

represents fourth derivative of

f (x)

at

x = 0

) is equal to

MEDIUM

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Proficiency in 'dy/dx as a Rate Measurer & Tangents, Normals' Exercise 1>Q 4

The curve

x + y - \ln (x + y) = 2 x + 5

has a vertical tangent at the point

(α, β)

, then

α + β

is equal to

HARD

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Proficiency in 'dy/dx as a Rate Measurer & Tangents, Normals' Exercise 1>Q 5

Let

y = f (x), f : R \to R

be an odd differentiable function such that

f^{'''} (x) > 0

and

g (α, β) = s i n^{8} α + c o s^{8} β + 2 - 4 s i n^{2} α \cdot c o s^{2} β

.
If

f^{''} (g (α, β)) = 0

, then

{s i n}^{2} α + {s i n}^{2} β

is equal to:

HARD

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Proficiency in 'dy/dx as a Rate Measurer & Tangents, Normals' Exercise 1>Q 6

A polynomial of

6^{th}

degree

f (x)

satisfies

f (x) = f (2 - x), \forall x \in R,

if

f (x) = 0

has

4

distinct and two equal roots, then sum of the roots of

f (x) = 0

is

MEDIUM

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Proficiency in 'dy/dx as a Rate Measurer & Tangents, Normals' Exercise 1>Q 7

A curve

y = f (x), f (x) \geq 0, \forall x \in R

has the property that for every point

P

on the curve length of subnormal is equal to abscissa of

P

. If

f (1) = 3

, then

f (4)

is equal to

MEDIUM

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Proficiency in 'dy/dx as a Rate Measurer & Tangents, Normals' Exercise 1>Q 8

If a variable tangent to the curve

x^{2} y = c^{3}

makes intercepts

a, b

on

x

and

y

axes respectively, then the value of

a^{2} b

is

HARD

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Proficiency in 'dy/dx as a Rate Measurer & Tangents, Normals' Exercise 1>Q 9

Let

f (x) = |\begin{matrix} 1 & 1 & 1 \\ 3 - x & 5 - 3 x^{2} & 3 x^{3} - 1 \\ 2 x^{2} - 1 & 3 x^{5} - 1 & 7 x^{8} - 1 \end{matrix}|

. Then, the equation

f (x) = 0

has

MEDIUM

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 7 - dy/dx as a Rate Measurer & Tangents, Normals>Proficiency in 'dy/dx as a Rate Measurer & Tangents, Normals' Exercise 1>Q 10

The graphs

y = 2 x^{3} - 4 x + 2

and

y = x^{3} + 2 x - 1

intersect at exactly three distinct points. The slope of the line passing through two of these points

Let $f (x)$ be a differentiable function in the interval $(0, 2)$ , then the value of $\int_{0}^{2} f (x) d x$

Important Questions on dy/dx as a Rate Measurer & Tangents, Normals

Learn and Prepare for any exam you want !

Let fx be a differentiable function in the interval 0,2, then the value of ∫02fxdx

Important Questions on dy/dx as a Rate Measurer & Tangents, Normals

Learn and Prepare for any exam you want !

Let $f (x)$ be a differentiable function in the interval $(0, 2)$ , then the value of $\int_{0}^{2} f (x) d x$