CA Foundation Exam > CA Foundation Questions > Choose the most appropriate option (a) (b) (c...
Start Learning for Free
Choose the most appropriate option (a) (b) (c) or (d)
The gradient of the curve y = 2x3 –3x2 – 12x +8 at x = 0 is
- a)–12
- b)12
- c)0
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Choose the most appropriate option (a) (b) (c) or (d)The gradient of t...
ANSWER :- a
Solution :- 2x^3 - 3x^2 -12x + 8 = 0
dy/dx = 6x^2 - 6x -12 = 0
(At x=0) = 6(0)^2 - 6(0) - 12
= -12
Most Upvoted Answer
Choose the most appropriate option (a) (b) (c) or (d)The gradient of t...
Finding the Gradient of a Curve
- The gradient of a curve at a particular point is the slope of the tangent to the curve at that point.
- To find the gradient of a curve at a point, we need to differentiate the equation of the curve with respect to x, and then substitute the value of x at the point of interest.
Given Curve and Point
- The given curve is y = 2x^3 - 3x^2 - 12x + 8.
- The point of interest is x = 0.
Differentiating the Curve
- To find the gradient at x = 0, we need to differentiate the curve with respect to x.
- The derivative of y = 2x^3 - 3x^2 - 12x + 8 is:
dy/dx = 6x^2 - 6x - 12
Substituting x = 0
- Now we need to substitute x = 0 in the derivative to find the gradient at x = 0.
- When we substitute x = 0 in the derivative, we get:
dy/dx = 6(0)^2 - 6(0) - 12 = -12
- Therefore, the gradient of the curve y = 2x^3 - 3x^2 - 12x + 8 at x = 0 is -12.
Answer
- The correct option is not given in the question, but option (a) 12 is incorrect.
- The correct answer is option (d) none of these, as the gradient at x = 0 is -12 and not 12.
- The gradient of a curve at a particular point is the slope of the tangent to the curve at that point.
- To find the gradient of a curve at a point, we need to differentiate the equation of the curve with respect to x, and then substitute the value of x at the point of interest.
Given Curve and Point
- The given curve is y = 2x^3 - 3x^2 - 12x + 8.
- The point of interest is x = 0.
Differentiating the Curve
- To find the gradient at x = 0, we need to differentiate the curve with respect to x.
- The derivative of y = 2x^3 - 3x^2 - 12x + 8 is:
dy/dx = 6x^2 - 6x - 12
Substituting x = 0
- Now we need to substitute x = 0 in the derivative to find the gradient at x = 0.
- When we substitute x = 0 in the derivative, we get:
dy/dx = 6(0)^2 - 6(0) - 12 = -12
- Therefore, the gradient of the curve y = 2x^3 - 3x^2 - 12x + 8 at x = 0 is -12.
Answer
- The correct option is not given in the question, but option (a) 12 is incorrect.
- The correct answer is option (d) none of these, as the gradient at x = 0 is -12 and not 12.
Free Test
FREE
| Start Free Test |
Community Answer
Choose the most appropriate option (a) (b) (c) or (d)The gradient of t...
Diff w.r.t.x
dy/dx = 2 d/dx x^3 - 3 d/dx x^2 - 12 d/dx x + d/dx 8
= 6x^2-6x-12
put x=0
=6*0-6*0-12
= -12
dy/dx = 2 d/dx x^3 - 3 d/dx x^2 - 12 d/dx x + d/dx 8
= 6x^2-6x-12
put x=0
=6*0-6*0-12
= -12
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
Choose the most appropriate option (a) (b) (c) or (d)The gradient of the curve y = 2x3 –3x2 – 12x +8 at x = 0 isa)–12b)12c)0d)none of theseCorrect answer is option 'A'. Can you explain this answer?
Question Description
Choose the most appropriate option (a) (b) (c) or (d)The gradient of the curve y = 2x3 –3x2 – 12x +8 at x = 0 isa)–12b)12c)0d)none of theseCorrect answer is option 'A'. 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 Choose the most appropriate option (a) (b) (c) or (d)The gradient of the curve y = 2x3 –3x2 – 12x +8 at x = 0 isa)–12b)12c)0d)none of theseCorrect answer is option 'A'. 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 Choose the most appropriate option (a) (b) (c) or (d)The gradient of the curve y = 2x3 –3x2 – 12x +8 at x = 0 isa)–12b)12c)0d)none of theseCorrect answer is option 'A'. Can you explain this answer?.
Choose the most appropriate option (a) (b) (c) or (d)The gradient of the curve y = 2x3 –3x2 – 12x +8 at x = 0 isa)–12b)12c)0d)none of theseCorrect answer is option 'A'. 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 Choose the most appropriate option (a) (b) (c) or (d)The gradient of the curve y = 2x3 –3x2 – 12x +8 at x = 0 isa)–12b)12c)0d)none of theseCorrect answer is option 'A'. 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 Choose the most appropriate option (a) (b) (c) or (d)The gradient of the curve y = 2x3 –3x2 – 12x +8 at x = 0 isa)–12b)12c)0d)none of theseCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Choose the most appropriate option (a) (b) (c) or (d)The gradient of the curve y = 2x3 –3x2 – 12x +8 at x = 0 isa)–12b)12c)0d)none of theseCorrect answer is option 'A'. 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 Choose the most appropriate option (a) (b) (c) or (d)The gradient of the curve y = 2x3 –3x2 – 12x +8 at x = 0 isa)–12b)12c)0d)none of theseCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Choose the most appropriate option (a) (b) (c) or (d)The gradient of the curve y = 2x3 –3x2 – 12x +8 at x = 0 isa)–12b)12c)0d)none of theseCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Choose the most appropriate option (a) (b) (c) or (d)The gradient of the curve y = 2x3 –3x2 – 12x +8 at x = 0 isa)–12b)12c)0d)none of theseCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Choose the most appropriate option (a) (b) (c) or (d)The gradient of the curve y = 2x3 –3x2 – 12x +8 at x = 0 isa)–12b)12c)0d)none of theseCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Choose the most appropriate option (a) (b) (c) or (d)The gradient of the curve y = 2x3 –3x2 – 12x +8 at x = 0 isa)–12b)12c)0d)none of theseCorrect answer is option 'A'. 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