CA Foundation Exam > CA Foundation Questions > The slope of the tangent to the curve y = x2-...
Start Learning for Free
The slope of the tangent to the curve y = x2-x at the point, where the line y= 2 cuts the curve in the first quadrant, is
- a)2
- b)3
- c)-3
- d)-2
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
The slope of the tangent to the curve y = x2-x at the point, where the...
Finding the Point of Intersection
To find the point of intersection of the line y= 2 and the curve y = x2-x, we can equate the two equations and solve for x.
2 = x2-x
Rearranging the equation, we get:
x2 - x - 2 = 0
This is a quadratic equation that can be solved using the quadratic formula:
x = (-b ± √(b2-4ac))/2a
Plugging in the values, we get:
x = (1 ± √(1+8))/2
x = (1 ± √9)/2
x = (1 ± 3)/2
So, x = -1 or x = 2. Since we are looking for the point of intersection in the first quadrant, we can take x = 2.
Therefore, the point of intersection is (2, 2).
Finding the Slope of the Tangent
To find the slope of the tangent to the curve y = x2-x at the point (2, 2), we need to take the derivative of the function and evaluate it at x = 2.
y = x2-x
dy/dx = 2x-1
At x = 2,
dy/dx = 2(2)-1 = 3
Therefore, the slope of the tangent to the curve y = x2-x at the point (2, 2) is 3.
Answer: Option B (3)
To find the point of intersection of the line y= 2 and the curve y = x2-x, we can equate the two equations and solve for x.
2 = x2-x
Rearranging the equation, we get:
x2 - x - 2 = 0
This is a quadratic equation that can be solved using the quadratic formula:
x = (-b ± √(b2-4ac))/2a
Plugging in the values, we get:
x = (1 ± √(1+8))/2
x = (1 ± √9)/2
x = (1 ± 3)/2
So, x = -1 or x = 2. Since we are looking for the point of intersection in the first quadrant, we can take x = 2.
Therefore, the point of intersection is (2, 2).
Finding the Slope of the Tangent
To find the slope of the tangent to the curve y = x2-x at the point (2, 2), we need to take the derivative of the function and evaluate it at x = 2.
y = x2-x
dy/dx = 2x-1
At x = 2,
dy/dx = 2(2)-1 = 3
Therefore, the slope of the tangent to the curve y = x2-x at the point (2, 2) is 3.
Answer: Option B (3)
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
The slope of the tangent to the curve y = x2-x at the point, where the line y= 2 cuts the curve in the first quadrant, isa)2b)3c)-3d)-2Correct answer is option 'B'. Can you explain this answer?
Question Description
The slope of the tangent to the curve y = x2-x at the point, where the line y= 2 cuts the curve in the first quadrant, isa)2b)3c)-3d)-2Correct answer is option 'B'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The slope of the tangent to the curve y = x2-x at the point, where the line y= 2 cuts the curve in the first quadrant, isa)2b)3c)-3d)-2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The slope of the tangent to the curve y = x2-x at the point, where the line y= 2 cuts the curve in the first quadrant, isa)2b)3c)-3d)-2Correct answer is option 'B'. Can you explain this answer?.
The slope of the tangent to the curve y = x2-x at the point, where the line y= 2 cuts the curve in the first quadrant, isa)2b)3c)-3d)-2Correct answer is option 'B'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The slope of the tangent to the curve y = x2-x at the point, where the line y= 2 cuts the curve in the first quadrant, isa)2b)3c)-3d)-2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The slope of the tangent to the curve y = x2-x at the point, where the line y= 2 cuts the curve in the first quadrant, isa)2b)3c)-3d)-2Correct answer is option 'B'. Can you explain this answer?.
Solutions for The slope of the tangent to the curve y = x2-x at the point, where the line y= 2 cuts the curve in the first quadrant, isa)2b)3c)-3d)-2Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of The slope of the tangent to the curve y = x2-x at the point, where the line y= 2 cuts the curve in the first quadrant, isa)2b)3c)-3d)-2Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The slope of the tangent to the curve y = x2-x at the point, where the line y= 2 cuts the curve in the first quadrant, isa)2b)3c)-3d)-2Correct answer is option 'B'. Can you explain this answer?, a detailed solution for The slope of the tangent to the curve y = x2-x at the point, where the line y= 2 cuts the curve in the first quadrant, isa)2b)3c)-3d)-2Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of The slope of the tangent to the curve y = x2-x at the point, where the line y= 2 cuts the curve in the first quadrant, isa)2b)3c)-3d)-2Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The slope of the tangent to the curve y = x2-x at the point, where the line y= 2 cuts the curve in the first quadrant, isa)2b)3c)-3d)-2Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Suggested Free Tests
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!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup