Mechanical Engineering Exam > Mechanical Engineering Questions > A point on a curve is said to be an extremum ...
Start Learning for Free
A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct exterma for the curve 3x4 – 16x3 – 24x2 + 37 is
- a)0
- b)1
- c)2
- d)3
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A point on a curve is said to be an extremum if it is a local minimum ...
Most Upvoted Answer
A point on a curve is said to be an extremum if it is a local minimum ...
The first step to find the extrema of a curve is to find its derivative and then look for the points where the derivative is zero or undefined. So, let's find the derivative of the given curve:
f(x) = 3x^4
f'(x) = 12x^3
Now, we need to find the points where f'(x) is zero or undefined:
12x^3 = 0
x = 0
Since f'(x) is defined for all x, there are no points where it is undefined. Therefore, the only point where f'(x) is zero is x = 0.
To determine whether this point is a local minimum or a local maximum, we need to look at the sign of f''(x) at x = 0:
f''(x) = 36x^2
f''(0) = 0
Since f''(0) = 0, we cannot determine the type of extremum at x = 0 using the second derivative test. Instead, we need to look at the behavior of f(x) near x = 0.
If we look at the graph of f(x) = 3x^4, we can see that it is a even function, which means that it is symmetric about the y-axis. This means that f(x) has a local minimum at x = 0, since the curve approaches 0 from both sides and goes upward.
Therefore, the curve has one local minimum at x = 0, and no local maximums.
f(x) = 3x^4
f'(x) = 12x^3
Now, we need to find the points where f'(x) is zero or undefined:
12x^3 = 0
x = 0
Since f'(x) is defined for all x, there are no points where it is undefined. Therefore, the only point where f'(x) is zero is x = 0.
To determine whether this point is a local minimum or a local maximum, we need to look at the sign of f''(x) at x = 0:
f''(x) = 36x^2
f''(0) = 0
Since f''(0) = 0, we cannot determine the type of extremum at x = 0 using the second derivative test. Instead, we need to look at the behavior of f(x) near x = 0.
If we look at the graph of f(x) = 3x^4, we can see that it is a even function, which means that it is symmetric about the y-axis. This means that f(x) has a local minimum at x = 0, since the curve approaches 0 from both sides and goes upward.
Therefore, the curve has one local minimum at x = 0, and no local maximums.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
Top Courses for Mechanical Engineering
Question Description
A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct exterma for the curve 3x4 – 16x3 – 24x2 + 37 isa)0 b)1 c)2 d)3Correct answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct exterma for the curve 3x4 – 16x3 – 24x2 + 37 isa)0 b)1 c)2 d)3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct exterma for the curve 3x4 – 16x3 – 24x2 + 37 isa)0 b)1 c)2 d)3Correct answer is option 'D'. Can you explain this answer?.
A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct exterma for the curve 3x4 – 16x3 – 24x2 + 37 isa)0 b)1 c)2 d)3Correct answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct exterma for the curve 3x4 – 16x3 – 24x2 + 37 isa)0 b)1 c)2 d)3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct exterma for the curve 3x4 – 16x3 – 24x2 + 37 isa)0 b)1 c)2 d)3Correct answer is option 'D'. Can you explain this answer?.
Solutions for A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct exterma for the curve 3x4 – 16x3 – 24x2 + 37 isa)0 b)1 c)2 d)3Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct exterma for the curve 3x4 – 16x3 – 24x2 + 37 isa)0 b)1 c)2 d)3Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct exterma for the curve 3x4 – 16x3 – 24x2 + 37 isa)0 b)1 c)2 d)3Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct exterma for the curve 3x4 – 16x3 – 24x2 + 37 isa)0 b)1 c)2 d)3Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct exterma for the curve 3x4 – 16x3 – 24x2 + 37 isa)0 b)1 c)2 d)3Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct exterma for the curve 3x4 – 16x3 – 24x2 + 37 isa)0 b)1 c)2 d)3Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Signup to solve all Doubts
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