Find the best tutors and institutes for Class 12 Tuition
Application of Derivatives EXERCISE 6.2 Solutions
- Q1: Show that the function given by $f(x) = 3x + 17$ is increasing on R.
- Q2: Show that the function given by $f(x) = e^{2x}$ is increasing on R.
- Q3(a): Show that the function given by $f(x) = \sin x$ is (a) increasing in $(0, \frac{\pi}{2})$
- Q3(b): Show that the function given by $f(x) = \sin x$ is (b) decreasing in $(\frac{\pi}{2}, \pi)$
- Q3(c): Show that the function given by $f(x) = \sin x$ is (c) neither increasing nor decreasing in $(0, \pi)$
- Q4(a): Find the intervals in which the function $f$ given by $f(x) = 2x^2 – 3x$ is (a) increasing
- Q4(b): Find the intervals in which the function $f$ given by $f(x) = 2x^2 – 3x$ is (b) decreasing
- Q5(a): Find the intervals in which the function $f$ given by $f(x) = 2x^3 – 3x^2 – 36x + 7$ is (a) increasing
- Q5(b): Find the intervals in which the function $f$ given by $f(x) = 2x^3 – 3x^2 – 36x + 7$ is (b) decreasing
- Q6(a): Find the intervals in which the following functions are strictly increasing or decreasing: (a) $x^2 + 2x – 5$
- Q6(b): Find the intervals in which the following functions are strictly increasing or decreasing: (b) $10 – 6x – 2x^2$
- Q6(c): Find the intervals in which the following functions are strictly increasing or decreasing: (c) $–2x^3 – 9x^2 – 12x + 1$
- Q6(d): Find the intervals in which the following functions are strictly increasing or decreasing: (d) $6 – 9x – x^2$
- Q6(e): Find the intervals in which the following functions are strictly increasing or decreasing: (e) $(x + 1)^3 (x – 3)^3$
- Q7: Show that $y = \log(1 + x) - \frac{2x}{2+x}$, $x > – 1$, is an increasing function of $x$ throughout its domain.
- Q8: Find the values of $x$ for which $y = [x(x – 2)]^2$ is an increasing function.
- Q9: Prove that $y = \frac{4\sin\theta}{(2 + \cos\theta)} - \theta$ is an increasing function of $\theta$ in $[0, \frac{\pi}{2}]$.
- Q10: Prove that the logarithmic function is increasing on $(0, \infty)$.
- Q11: Prove that the function $f$ given by $f(x) = x^2 – x + 1$ is neither strictly increasing nor decreasing on $(– 1, 1)$.
- Q12: Which of the following functions are decreasing on $(0, \frac{\pi}{2})$ ?
- Q13: On which of the following intervals is the function $f$ given by $f(x) = x^{100} + \sin x –1$ decreasing ?
- Q14: For what values of $a$ the function $f$ given by $f(x) = x^2 + ax + 1$ is increasing on $[1, 2]$?
- Q15: Let $I$ be any interval disjoint from $[–1, 1]$. Prove that the function $f$ given by $f(x) = x + \frac{1}{x}$ is increasing on $I$.
- Q16: Prove that the function $f$ given by $f(x) = \log \sin x$ is increasing on $(0, \frac{\pi}{2})$ and decreasing on $(\frac{\pi}{2}, \pi)$.
- Q17: Prove that the function $f$ given by $f(x) = \log |\cos x|$ is decreasing on $(0, \frac{\pi}{2})$ and increasing on $(\frac{3\pi}{2}, 2\pi)$.
- Q18: Prove that the function given by $f(x) = x^3 – 3x^2 + 3x – 100$ is increasing in R.
- Q19: The interval in which $y = x^2 e^{–x}$ is increasing is
Other Exercises for CBSE - Class 12 Mathematics Application of Derivatives
Chapters in CBSE - Class 12 Mathematics
Top Tutors who teach Application of Derivatives
Top Tutor 
Sector 54, Chandigarh 
15 yrs of Exp 
10 students 
353 hrs of classes completed 
750 per hour 
Online Classes i am physics teacher with 15 years of experience in teaching 11,12, competitive exams. i always try to explain topics more in practical form rather than theortical by giving examples from day to day life . topics like electrostatics , alternating current ,optics , semiconductors and logic gates are most imp and students usually got troubled there but with practical apporoach i make them go with happy and easy learning .
Puts in genuine effort Clear concepts Offer flexible timings Cover all types of questions in class Excellent teacher
Top Tutor Bade Kajipur, Gorakhpur 20 yrs of Exp 7 students 1221 hrs of classes completed 350 per hour Online Classes 
Student's Home 
Tutor's home l am Physics teacher,usually I teach class 11, 12 and competitive exam like NEET and JEE teaching offline classes since 2004 and online classes since 2020, My Students Raunak singh in 2023 Crack NEET with AIR 555 score 695/720, and he scored 99/100 in Class 12 ISC Board and Aditi Srivastava in 2022 Crack NEET in first attempt score 621/720, and she scored 95/100 in class 12 CBSE Board. Received Appreciation Letter from HRD Minister(Central Government) Smriti Zubin Irani My proficiency is in physics. Advika, If you want online physics class through Urbanpro platform, please let me know. Monthly Fees 4000/- for 3 days in a week and in a month 12 hours Every Live Class is of 1hour , including Precise Notes of each topic Practice Questions and Online Test With Video Solutions. Formula Sheet for every chapter. Course Fees of NEET 2025 Crash Course for Physics is 12000/- I prefer to teach physics specially class 11 and 12, I do focus on Competitive level Physics like N.E.E.T. and I.I.T.J.E.E. along with basic physics to make my students understand physics easier. My focus is on competitive exam for betterment of students. I have been teaching Physics twenty years of teaching experience, I had done my schooling and college from Gorakhpur city Uttar Pradesh. I am Teaching since 2004 in Gorakhpur initially off-line, and teaching online since 2020. I do provide study material like Notes, Question Bank and D.P.P., No Additional charge is require to pay, it is included in class fees. 4000/- for 3 days in a week and in a month 12 hours l am Physics teacher,usually I teach class 11, 12 and competitive exam like NEET and JEE teaching offline classes since 2004 and online classes since 2020, My proficiency is in physics. I have received a letter of appreciation from the HRD ministry of the central government of India.
He's one of the most exceptional teacher, I have ever been a student of. Sir teaches in such a way that you can imagine it in your mind, and the concepts never leave you. I was scared of physics earlier, but now I am able to solve questions with much ease and much more confident in it.
Top Tutor Domalguda, Hyderabad 2 yrs of Exp 3 students 79 hrs of classes completed 299 per hour Online Classes Tutor's home I am accountancy tutor with teaching experience of 2yrs.i come from a very strong commerce background and I have passion towards accountancy teaching .I would like to solve challenging problems that students face in this field.
Shes a very good tutor and answered my doubts at any time even if it’s late or early. Definitely would recommend her.
Top Tutor G.T. Road, Ballabgarh 7 yrs of Exp 9 students 389 hrs of classes completed 500 per hour Online Classes I have done MTECH in ECE from YMCA university faridabad and BTECH from DIT university Dehradun. I Have been teaching BTECH ECE students for last 8 Years and Physics to students of class XI and XII for last 7 years. Physics has always excited me and its wonderful to be associated with physics & Besides, Teaching Physics imparts a sense of satisfaction to me. I have been giving home/online tutions to students of various schools in faridabad region. I also teach Maths to students of class IX an X. I have Published research papers based on Routing in Cognitive Networks in International Journals . Besides being an Educator I am Mentor/Counselor in the same College.
Top Tutor Andheri West, Mumbai 10 yrs of Exp 8 students 106 hrs of classes completed 1000 per hour Online Classes Student's Home I have over 10 years of teaching experience in reputed schools and colleges, where I have taught students across different academic levels with a strong focus on conceptual clarity and practical understanding. Throughout my career, I have handled diverse classrooms, adapting my teaching methods to suit students’ learning styles and academic needs. In school education, I have taught core subjects aligned with the curriculum, ensuring students build a strong foundation and perform confidently in examinations. I have extensive experience in lesson planning, syllabus completion, exam preparation, conducting assessments, and providing individual attention to students who need additional support.
Other Subjects in CBSE - Class 12
Download free CBSE - Class 12 Mathematics Application of Derivatives EXERCISE 6.2 worksheets
Download Now
