RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiability

RD Sharma Solutions for Class 12 Maths Chapter 10 – Free PDF Download

The RD Sharma Solutions for Class 12 Maths Chapter 10 – Differentiability is provided here for the benefit of the students. To achieve a good academic score in Mathematics, the important thing to be done by the students is to practice all the questions of each and every exercise. Students can score good marks in the exams by solving and cross-checking the answers with the RD Sharma Solutions prepared by BYJU’S experts in Maths.

RD Sharma Solutions for Class 12 Maths are focused on learning various mathematical tricks and shortcuts for quick and easy calculations. These solutions are in accordance with the latest CBSE syllabus and marking schemes. Students can easily get the PDF of RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiability from the given links.

Let us have a look at some of the important concepts that are discussed in the RD Sharma Solutions of this chapter.

  • Differentiability at a point
  • Definition and meaning of differentiability at a point
  • Differentiability in a set
  • Some useful results on differentiability

RD Sharma Solutions For Class 12 Maths Chapter 10 Differentiability:-Download PDF Here

RD Sharma Class 12 Maths Solutions Chapter 10 Differentibaility
RD Sharma Class 12 Maths Solutions Chapter 10 Differentibaility 1
RD Sharma Class 12 Maths Solutions Chapter 10 Differentibaility 2
RD Sharma Class 12 Maths Solutions Chapter 10 Differentibaility 3
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RD Sharma Class 12 Maths Solutions Chapter 10 Differentibaility 5
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RD Sharma Class 12 Maths Solutions Chapter 10 Differentibaility 9
RD Sharma Class 12 Maths Solutions Chapter 10 Differentibaility 10
RD Sharma Class 12 Maths Solutions Chapter 10 Differentibaility 11
RD Sharma Class 12 Maths Solutions Chapter 10 Differentibaility 12

Access answers to Maths RD Sharma Solutions For Class 12 Chapter 10 – Differentiability

Exercise 10.1 Page No: 10.10

1. Show that f (x) = |x – 3| is continuous but not differentiable at x = 3.

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 1
RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 2

2. Show that f (x) = x 1/3 is not differentiable at x = 0.

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 3
RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 4

Since, LHD and RHD does not exist at x = 0

Hence, f(x) is not differentiable at x = 0

RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 5

Solution:

Now we have to check differentiability of given function at x = 3

That is LHD (at x = 3) = RHD (at x = 3)

RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 6

= 12

Since, (LHD at x = 3) = (RHD at x = 3)

Hence, f(x) is differentiable at x = 3.

4. Show that the function f is defined as follows

RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 7

Is continuous at x = 2, but not differentiable thereat.

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 8

Since, LHL = RHL = f (2)

Hence, F(x) is continuous at x = 2

Now we have to differentiability at x = 2

RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 9

= 5

Since, (RHD at x = 2) ≠ (LHD at x = 2)

Hence, f (2) is not differentiable at x = 2.

5. Discuss the continuity and differentiability of the function f (x) = |x| + |x -1| in the interval of (-1, 2).

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 10

We know that a polynomial and a constant function is continuous and differentiable everywhere. So, f(x) is continuous and differentiable for x ∈

(-1, 0) and x ∈ (0, 1) and (1, 2).

We need to check continuity and differentiability at x = 0 and x = 1.

Continuity at x = 0

RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 11

Since, f(x) is continuous at x = 1

Now we have to check differentiability at x = 0

For differentiability, LHD (at x = 0) = RHD (at x = 0)

Differentiability at x = 0

RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 12

Since, (LHD at x = 0) ≠ (RHD at x = 0)

So, f(x) is differentiable at x = 0.

Now we have to check differentiability at x = 1

For differentiability, LHD (at x = 1) = RHD (at x = 1)

Differentiability at x = 1

RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 13

Since, f(x) is not differentiable at x = 1.

So, f(x) is continuous on (- 1, 2) but not differentiable at x = 0, 1

Exercise 10.2 Page No: 10.16

1. If f is defined by f (x) = x2, find f’ (2).

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 14

2. If f is defined by f (x) = x2 – 4x + 7, show that f’ (5) = 2 f’ (7/2)

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 15
RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 16

Hence the proof.

3. Show that the derivative of the function f is given by f (x) = 2x3 – 9x2 + 12 x + 9, at x = 1 and x = 2 are equal.

Solution:

We are given with a polynomial function f(x) = 2x3 – 9x2 + 12x + 9, and we have

RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 17

4. If for the function Ø (x) = λ x2 + 7x – 4, Ø’ (5) = 97, find λ.

Solution:

We have to find the value of λ given in the real function and we are given with the differentiability of the function f(x) = λx2 + 7x – 4 at x = 5 which is f ‘(5) = 97, so we will adopt the same process but with a little variation.

RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 18

5. If f (x) = x3 + 7x2 + 8x – 9, find f’ (4).

Solution:

We are given with a polynomial function f(x) = x3 + 7x2 + 8x – 9, and we have to find whether it is derivable at x = 4 or not,

RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 19
RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 20

6. Find the derivative of the function f defined by f (x) = mx + c at x = 0.

Solution:

We are given with a polynomial function f(x) = mx + c, and we have to find whether it is derivable at x = 0 or not,

RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiablity Image 21

This is the derivative of a function at x = 0, and also this is the derivative of this function at every value of x.

Also, access RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiability

Exercise 10.1 Solutions

Exercise 10.2 Solutions

Frequently Asked Questions on RD Sharma Solutions for Class 12 Maths Chapter 10

Which is the best reference guide for Class 12 exam preparation?

RD Sharma Solutions for Class 12 Maths Chapter 10 is the best reference material for CBSE board exam preparation. Subject experts have framed and solved the questions from every section. Studying from these books will ensure that they can easily excel in their final exams. The books are completely based on the exam-oriented approach to help students score well in their board examination. After completing the textbook questions, students can move on to previous year question papers and sample papers for a better idea of the exam pattern.

Where can I get the correct Solutions for RD Sharma Class 12 Maths Chapter 10?

Students and teachers can access BYJU’S official website for RD Sharma Solutions Class 12 Maths Chapter 10 which provides a wide range of study materials like text books, reference books etc. The solutions are prepared with utmost care to help students understand the concepts easily and score well in their board exams.

How to achieve good marks by referring to RD Sharma Class 12 Maths Chapter 10?

By referring to RD Sharma Solutions for Class 12 Maths Chapter 10 available at BYJU’S website, students can achieve high marks in the main exams. Students are required to go through RD Sharma Solutions thoroughly before the final exams to score well and intensify their question-solving abilities. Practice is an essential task to learn and score well in Maths.

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