Welcome to Class 12 Applied Maths Chapter 6, where we embark on an exciting journey into the world of advanced mathematical concepts tailored for Class 11 students.” Unlock the power of applied mathematics with expert solutions crafted by professionals at AppliedMath.com. Designed to propel students towards academic success, our meticulously curated ML Aggarwal Solutions for Applied Mathematics cater to Class 11 and class 12 students seeking mastery in their examinations. Every query from the CBSE ML Aggarwal Books finds a comprehensive answer on our platform, complete with detailed explanations and step-by-step solutions presented in an easily understandable language.
Dive into the world of applied mathematics and discover how our resources can elevate your understanding and performance. Keep reading to explore the wealth of ML Aggarwal Solutions for Class 11 and Class 12 Applied Mathematics.
Here we provide you with Class 12 Applied Maths Chapter 6, to help you again a comprehensive understanding of the chapter and its concepts.
https://appliedmathsolution.com/wp-admin/post.php?post=6&action=edit
Class 12 Applied Maths Chapter 6 Solutions
Application of Derivatives
EXERCISE- 6.3
Q.1 Solve for x:
(i) x(x – 2) (x – 5) (x + 3) > 0
(ii) x^4 – 5x^2 + 4 ≥ 0
Ans. (i) x(x – 2) (x – 5) (x + 3) > 0
x = 0, 2, 5, -3
(ii) x^4 – 5x^2 + 4 ≥ 0
(x^2)^2 – 5x^2 + 4 ≥ 0
Taking x^2 = a
a^2 – 5a + 4 ≥ 0
a^4 – 4a – a + 4 ≥ 0
a (a – 4) – 1 (a – 4) ≥ 0
(a – 1) (a – 4) ≥ 0
x^2 – 1) (x^2 – 4) ≥ 0
(x + 1) (x – 1) ( x + 2) (x – 2) ≥ 0
x = -1, 1, -2, 2
Q.2 Find all real values of x which satisfy
(i) x^3(x – 1) (x – 2) > 0
(ii) x^2(x – 1) (x – 2) ≤ 0
Ans. (i) x^3(x – 1) (x – 2) > 0
x = 0, 1, 2
(ii) x^2(x – 1) (x – 2) ≤ 0
x = 0, 1, 2
Q.3 Solve for x:
(i) 1/(x – 2) ≤ 1
(ii) [(x + 1) (x – 3)]/(x + 2) ≥ 0
Ans. (i) 1/(x – 2) ≤ 1, x – 2 ≠ 0, x ≠ 2
1/(x -2) – 1 ≤ 0
(1 – x + 2)/(x – 2) ≤ 0
(-x + 3)/(x – 2) ≤ 0
multiplying (x – 2) in numerator and denominator
[(-x + 3) (x – 2)]/(x – 2)^2 ≤ 0
So, x = 2, 3
(ii) [(x + 1) (x – 3)]/(x + 2) ≥ 0
[(x + 1) (x – 3)]/(x + 2) ≥ 0, x + 2 ≠ 0, x ≠ -2
[(x + 1)(x – 3)(x + 2)]/(x + 2)^2 ≥ 0
x = -1, 3, -2
FAQ’s related to Class 12 Applied Maths Chapter 6 on Application of Derivatives :
Q.1 What are the main applications of derivatives?
Ans. Derivatives have the following applications:
(i) Finding approximations using differentials.
(ii) Finding rate of change of a quantity.
(iii) Determining tangents and normals to a curve.
(iv) Solving optimization problems (maximum and minimum values).
(v) Identifying the increasing or decreasing nature of functions.
Q.2 How do you find the rate of change of a quantity?
Ans. The rate of change of a quantity y with respect to another quantity xxx is given by dy/dx. This represents how y changes as x varies.
Q.3 What is the geometrical significance of a derivative?
Ans. The derivative dy/dx represents the slope of the tangent to the curve at a given point. It indicates how steep the curve is at that point.
Q.4 What are tangents and normals, and how are they calculated?
Ans. A tangent is a line that touches a curve at one point without crossing it.
A normal is a line perpendicular to the tangent at the point of contact.
Slope of normal: m(n) = −1/m(t)
Slope of tangent: m(t) = dy/dx at the given point.
These are a few Frequently Asked Questions relating to Class 12 Applied Maths Chapter 13
In Class 12 Applied Maths chapter 6, you will explore fascinating topics that form the backbone of practical problem-solving techniques. Through clear explanations, illustrative examples, and step-by-step solutions, you’ll grasp complex concepts effortlessly. Whether you’re preparing for exams or simply eager to deepen your mathematical understanding, Class 12 Applied Maths Chapter 6 promises an enriching learning experience that will set you on the path to success. Class 12 Applied Maths Chapter 6, we delve deep into advanced mathematical concepts that are crucial for understanding.
