JEE Exam > JEE Questions > f (x) = max {x, x3},then the number of points...
Start Learning for Free
f (x) = max {x, x3},then the number of points where f (x) is not differentiable, are
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
f (x) = max {x, x3},then the number of points where f (x) is not diffe...
Solution:
To find the points where the given function is not differentiable, we need to find the points where the function is not continuous or where the derivative does not exist.
Step 1: Finding the points of non-differentiability where the function is not continuous.
Since the function is the maximum of two functions, we need to consider the points where these two functions are equal.
Let x = x³, then x³ - x = 0, which gives x = 0, 1.
Therefore, the function is not continuous at x = 0 and x = 1.
Step 2: Finding the points of non-differentiability where the derivative does not exist.
At x = 0, the left-hand derivative is 1 and the right-hand derivative is 0.
At x = 1, the left-hand derivative is 3 and the right-hand derivative is 0.
Therefore, the function is not differentiable at x = 0 and x = 1.
Hence, the function f(x) = max{x, x³} is not differentiable at three points, namely x = 0, x = 1, and wherever the function changes from x to x³ or vice versa.
Therefore, the correct option is (C) 3.
To find the points where the given function is not differentiable, we need to find the points where the function is not continuous or where the derivative does not exist.
Step 1: Finding the points of non-differentiability where the function is not continuous.
Since the function is the maximum of two functions, we need to consider the points where these two functions are equal.
Let x = x³, then x³ - x = 0, which gives x = 0, 1.
Therefore, the function is not continuous at x = 0 and x = 1.
Step 2: Finding the points of non-differentiability where the derivative does not exist.
At x = 0, the left-hand derivative is 1 and the right-hand derivative is 0.
At x = 1, the left-hand derivative is 3 and the right-hand derivative is 0.
Therefore, the function is not differentiable at x = 0 and x = 1.
Hence, the function f(x) = max{x, x³} is not differentiable at three points, namely x = 0, x = 1, and wherever the function changes from x to x³ or vice versa.
Therefore, the correct option is (C) 3.
Free Test
FREE
| Start Free Test |
Community Answer
f (x) = max {x, x3},then the number of points where f (x) is not diffe...
f(x)=m{x,x3}
= x;x<−1 and
= x3;−1≤x≤0
⇒ f(x)=x;0≤x≤1 and
= x3;x≥1
∴ f(x)=1;x<−1
∴ f′(x)=3x2;− 1≤x≤0 and =1
0<x<1
Hence answer is 3
= x;x<−1 and
= x3;−1≤x≤0
⇒ f(x)=x;0≤x≤1 and
= x3;x≥1
∴ f(x)=1;x<−1
∴ f′(x)=3x2;− 1≤x≤0 and =1
0<x<1
Hence answer is 3
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
Question Description
f (x) = max {x, x3},then the number of points where f (x) is not differentiable, area)1b)2c)3d)4Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about f (x) = max {x, x3},then the number of points where f (x) is not differentiable, area)1b)2c)3d)4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for f (x) = max {x, x3},then the number of points where f (x) is not differentiable, area)1b)2c)3d)4Correct answer is option 'C'. Can you explain this answer?.
f (x) = max {x, x3},then the number of points where f (x) is not differentiable, area)1b)2c)3d)4Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about f (x) = max {x, x3},then the number of points where f (x) is not differentiable, area)1b)2c)3d)4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for f (x) = max {x, x3},then the number of points where f (x) is not differentiable, area)1b)2c)3d)4Correct answer is option 'C'. Can you explain this answer?.
Solutions for f (x) = max {x, x3},then the number of points where f (x) is not differentiable, area)1b)2c)3d)4Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of f (x) = max {x, x3},then the number of points where f (x) is not differentiable, area)1b)2c)3d)4Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
f (x) = max {x, x3},then the number of points where f (x) is not differentiable, area)1b)2c)3d)4Correct answer is option 'C'. Can you explain this answer?, a detailed solution for f (x) = max {x, x3},then the number of points where f (x) is not differentiable, area)1b)2c)3d)4Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of f (x) = max {x, x3},then the number of points where f (x) is not differentiable, area)1b)2c)3d)4Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice f (x) = max {x, x3},then the number of points where f (x) is not differentiable, area)1b)2c)3d)4Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup