RD Sharma Solutions for Class 12 Maths Chapter 10 Differentiability

In order to gain 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. The students can score good marks in the exams by solving all the questions 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 Mathematics tricks and shortcuts for quick and easy calculations. 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 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
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RD Sharma Class 12 Maths Solutions Chapter 10 Differentibaility 10
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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
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Since, LHD and RHD does not exist at x = 0

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

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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:

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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

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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.

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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,

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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,

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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

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