Mathematics class 12 Applications of Derivatives Increasing and Decreasing Functions

Mathematics Class XII Applications of Derivatives Increasing and Decreasing Functions

Q. Find the intervals in which the function $f$ given by $f(x)=x^2−4x+6$ is (a) strictly increasing (b) strictly decreasing

(a) strictly decreasing in interval $(0,∞)$
(b) strictly increasing in the interval $(−∞,0)$

(a) strictly increasing in interval $(0,∞)$
(b) strictly decreasing in the interval $(−∞,0)$

(a) strictly increasing in interval $(2,∞)$
(b) strictly decreasing in the interval $(−∞,2)$

(a) strictly decreasing in interval $(2,∞)$
(b) strictly increasing in the interval $(−∞,2)$

Karnataka PU 2014

Q. Find the intervals in which the function $f$ given by $f(x)=2x^2− 3x$ is (a) strictly increasing (b) strictly decreasing

(a) strictly decreasing in interval $(4,∞)$
(b) strictly increasing in the interval $(−∞,3)$

(a) strictly increasing in interval $(\dfrac{3}{4},∞)$
(b) strictly decreasing in the interval $(−∞,\dfrac{3}{4})$

(a) strictly decreasing in interval $(\dfrac{3}{4},∞)$
(b) strictly increasing in the interval $(−∞,\dfrac{3}{4})$

(a) strictly increasing in interval $(0,∞)$
(b) strictly decreasing in the interval $(−∞,0)$

Karnataka PU 2016, 2019

Q. Find the intervals in which the function $f$ given by $f(x)=4x^3−6x^2-72x+30$ is (i) strictly increasing (ii) strictly decreasing.

During $(−∞, -2)$ and $(3, ∞)$, the function is strictly increasing.
During $(-2, 3)$, the function is strictly decreasing.

During $(−∞, -2)$, the function is strictly increasing.
During $(3, ∞)$, the function is strictly decreasing.

During $(−∞, 0)$, the function is strictly increasing.
During $(0, ∞)$, the function is strictly decreasing.

During $(−∞, -2)$ and $(3, ∞)$, the function is strictly decreasing.
During $(-2, 3)$, the function is strictly increasing.

Karnataka PU MQP 2023

OTHER CLASS XII TOPICS

Application of Integrals

Finding the area bounded by a curve

Applications of Derivatives

Applications of Derivatives

Increasing and Decreasing Functions

Maxima and Minima

Tangents and Normals

Continuity and Differentiability

Implicit and Explicit Differentiation

Order of equation

Slope of Tangent and Normal to curve

Determinants

Applications of Matrices - Solve System of Equations

Area of a triangle

Differential Equations

Differential Equations

Integration

Definite Integrals

Integral of the Type e^x[f(x) + Df(x)]dx

Integration by Partial Fractions

Integration by Parts

Integration of Particular Functions

Integration using Trignometric Identities

Linear Programming

Linear Programming

Matrices

Diagonal Matrix

Finding the missing number in a Matrix

Identity Matrix

Operations on Matrices

Symmetric and Skew Symmetric Matrices

Probability

Rational Numbers

Properties of Rational Numbers

Relations and Functions

Bijective Function

Binary Operation

Continuity of a Function

Equivalence Relation

Invertible Function

Reflexive Relation

Symmetric Relation

Transitive Relation

Types of Functions

Three Dimensional Geometry

Finding angle between line and plane

Finding the direction cosines

Finding the equation of line

Finding the equation of plane

Finding the intercepts of plane

Finding the shortest distance

Trigonometry

Inverse Trigonometric Functions

Vector Algebra

Area of parallelogram

Area of triangle

Finding the position vector of a point

Finding the projection of vector

Finding the unit vector

Negative of Vector

Operations on Vectors