Here we provide RD Sharma Class 12 Ex 10.2 Solutions Chapter 10 Differentiability for English medium students, Which will very helpful for every student in their exams. Students can download the RD Sharma Class 12 Ex 10.2 Solutions Chapter 10 Differentiability book pdf download. Now you will get step-by-step solutions to each question.
| Textbook | NCERT |
| Class | Class 12th |
| Subject | Maths |
| Chapter | 10 |
| Exercise | 10.2 |
| Category | RD Sharma Solutions |
RD Sharma Class 12 Ex 10.2 Solutions Chapter 10 Differentiability
Question 1. If f is defined by f(x) = x2, find f'(2).
Solution:
Hence, f'(2) = 4.
Question 2. If f is defined by f(x) = x2 – 4x + 7, show that f'(5) = 2f'(7/2).
Solution:
= 
f'(5) = 6 …….(1)
f'(7/2) = 3
⇒ 2f'(7/2) = 6 ……(2)
From (1) and (2)
f'(5) = 2f'(7/2).
Question 3. Show that the derivative of the function f given by f(x) = 2x3 – 9x2 +12x + 9 at x = 1 and x = 2 are equal.
Solution:
![= lim_{h\to0}\frac{[2(1+h)^2-9(1+h)^2+12(1+h)+9]-[2-9+12-9]}{h}](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-1b5140e22ff0127dcae50241df50dcc2_l3.svg "Rendered by QuickLaTeX.com")
⇒ f'(1) = 0
Now,
![= lim_{h\to0}\frac{[2(2+h)^3-9(2+h)^2+12(2+h)+9]-[16-36+24+9]}{h}](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-c6d41f85dd2b00d75d73819e3bb48a9d_l3.svg "Rendered by QuickLaTeX.com")
⇒ f'(2) = 0
Hence f'(1) = f'(2) = 0.
Question 4. If for the function f(x) = ax2 + 7x – 4, f'(5) = 97, find a.
Solution:
⇒ 97 = 10a +7
⇒ 10a = 90
⇒ a = 9
Question 5. If f(x) = x3 + 7x2 + 8x – 9, find f'(4).
Solution:
![= lim_{h\to0}\frac{[(4+h)^3+7(4+h)^2+8(4+h)-9]-[64+112+32-9]}{h}](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-dd486210fac4a345eb333c52cb3baccc_l3.svg "Rendered by QuickLaTeX.com")
![= lim_{h\to0}\frac{64+h^3+48h+12h^2+112+7h^2+56h+32+8h-9]-[210-9]}{h}](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-9c5c55cae69f0dbf174527377b3053ba_l3.svg "Rendered by QuickLaTeX.com")
⇒ f'(4) = 112
Question 6. Find the derivative of f(x) = mx + c at x = 0.
Solution:
⇒ f'(0) = m.
Question 7. Examine the differentiability of 
Solution:
Since f(x) is a polynomial function, it is continuous and differentiable everywhere.
Differentiability at x = –2
= 2
= 1
Since, LHD at x = –2 ≠ RHD at x = –2
Hence f(x) is not differentiable at x = –2.
Now, Differentiability at x = 0
(LHD at x = 0) 
= ∞
(RHD at x = 0)
= 1
Since, LHD at x = –2 ≠ RHD at x = 0
Hence f(x) is not differentiable at x = 0.
Question 8. Write an example of a function which is everywhere continuous but fails to be differentiable at exactly five points.
Solution:
We know the modulus function f(x) = |x| is continuous but not differentiable at x = 0.
Hence, f(x) = |x| + |x – 1| + |x – 2| + |x – 3| + |x – 4| is continuous but not fails to be differentiable at x = 0,1,2,3,4.
Question 9. Discuss the continuity and differentiability of f(x) = |log|x||.
Solution:
Graph of f(x) = |log|x||:
From the graph above, it is clear that f(x) is continuous everywhere, but not differentiable at 1 and -1.
Question 10. Discuss the continuity and differentiability of f(x) = e|x|.
Solution:
For continuity:
(LHL at x = 0) 
= 
= e0
= 1
(RHL at x = 0) 
= e0
= 1
Hence f(x) is continuous at x = 0.
For Differentiability:
(LHD at x = 0) = 
= –1
(RHD at x = 0) 
= 1
Thus, f(x) is not differentiable at x = 0.
Question 11. Discuss the differentiability of 
Solution:
(LHD at x = c) 
= k
(RHD at x = c) = 
= k
Clearly (LHD at x = c) = (RHD at x = c)
f(x) is differentiable at x = c.
Question 12. Is |sinx| differentiable? What about cos|x|?
Solution:
(LHD at x = nπ) 
= –1
(RHD at x = nπ) 
= 1
Since, LHD at x = nπ ≠ RHD at x = nπ
Hence f(x) = |sinx| is not differentiable at x = nπ.
Now, f(x) = cos|x|
Since, cos(–x) = cosx
Thus, f(x) = cos x
Hence f(x) = cos|x| is differentiable everywhere.
I think you got complete solutions for this chapter. If You have any queries regarding this chapter, please comment in the below section our subject teacher will answer you. We tried our best to give complete solutions so you got good marks in your exam.
If these solutions have helped you, you can also share rdsharmasolutions.in to your friends.