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The points on the curve 4 y = |x2−4| at which tangents are parallel to x – axis, are
- a)(4, 3) and (– 4, – 3)
- b)(0, 1) only
- c)(2, 0) and (– 2, 0)
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The points on the curve 4 y = |x2−4|at which tangents are parall...
Only when x = 0 and when x = 0 , y = 1. So, only at (0,1) tangent is parallel to x- axis.
Most Upvoted Answer
The points on the curve 4 y = |x2−4|at which tangents are parall...
Given curve: 4y = |x-24|
To find the points on the curve at which tangents are parallel to the x-axis, we need to find the points where the slope of the tangent is zero (since the slope of the x-axis is zero).
First, let's find the derivative of the curve:
Differentiating both sides of the equation with respect to x, we get:
4(dy/dx) = d/dx |x-24|
To find the derivative of the absolute value function, we consider two cases: x-24 > 0 and x-24 < />
Case 1: x-24 > 0
In this case, the absolute value function simplifies to x-24. Taking the derivative, we get:
4(dy/dx) = d/dx (x-24)
4(dy/dx) = 1
Case 2: x-24 < />
In this case, the absolute value function simplifies to -(x-24). Taking the derivative, we get:
4(dy/dx) = d/dx (-(x-24))
4(dy/dx) = -1
Simplifying both cases, we get:
Case 1: dy/dx = 1/4
Case 2: dy/dx = -1/4
Now, let's find the points on the curve where the slope of the tangent is zero (parallel to the x-axis).
Setting dy/dx = 0, we get:
Case 1: 1/4 = 0 (No solution)
Case 2: -1/4 = 0 (No solution)
Therefore, there are no points on the curve where the tangents are parallel to the x-axis. Hence, the correct answer is option 'D' (none of these).
Note: It is important to carefully analyze the given curve and consider all possible cases when finding the points where tangents are parallel to a particular line. In this case, since the slope of the x-axis is zero, we need to find the points where the derivative is zero. However, after considering all cases, we find that there are no such points on the given curve.
To find the points on the curve at which tangents are parallel to the x-axis, we need to find the points where the slope of the tangent is zero (since the slope of the x-axis is zero).
First, let's find the derivative of the curve:
Differentiating both sides of the equation with respect to x, we get:
4(dy/dx) = d/dx |x-24|
To find the derivative of the absolute value function, we consider two cases: x-24 > 0 and x-24 < />
Case 1: x-24 > 0
In this case, the absolute value function simplifies to x-24. Taking the derivative, we get:
4(dy/dx) = d/dx (x-24)
4(dy/dx) = 1
Case 2: x-24 < />
In this case, the absolute value function simplifies to -(x-24). Taking the derivative, we get:
4(dy/dx) = d/dx (-(x-24))
4(dy/dx) = -1
Simplifying both cases, we get:
Case 1: dy/dx = 1/4
Case 2: dy/dx = -1/4
Now, let's find the points on the curve where the slope of the tangent is zero (parallel to the x-axis).
Setting dy/dx = 0, we get:
Case 1: 1/4 = 0 (No solution)
Case 2: -1/4 = 0 (No solution)
Therefore, there are no points on the curve where the tangents are parallel to the x-axis. Hence, the correct answer is option 'D' (none of these).
Note: It is important to carefully analyze the given curve and consider all possible cases when finding the points where tangents are parallel to a particular line. In this case, since the slope of the x-axis is zero, we need to find the points where the derivative is zero. However, after considering all cases, we find that there are no such points on the given curve.
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The points on the curve 4 y = |x2−4|at which tangents are parallel to x – axis, area)(4, 3) and (– 4, – 3)b)(0, 1) onlyc)(2, 0) and (– 2, 0)d)none of theseCorrect answer is option 'B'. Can you explain this answer?
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The points on the curve 4 y = |x2−4|at which tangents are parallel to x – axis, area)(4, 3) and (– 4, – 3)b)(0, 1) onlyc)(2, 0) and (– 2, 0)d)none of theseCorrect answer is option 'B'. 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 The points on the curve 4 y = |x2−4|at which tangents are parallel to x – axis, area)(4, 3) and (– 4, – 3)b)(0, 1) onlyc)(2, 0) and (– 2, 0)d)none of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The points on the curve 4 y = |x2−4|at which tangents are parallel to x – axis, area)(4, 3) and (– 4, – 3)b)(0, 1) onlyc)(2, 0) and (– 2, 0)d)none of theseCorrect answer is option 'B'. Can you explain this answer?.
The points on the curve 4 y = |x2−4|at which tangents are parallel to x – axis, area)(4, 3) and (– 4, – 3)b)(0, 1) onlyc)(2, 0) and (– 2, 0)d)none of theseCorrect answer is option 'B'. 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 The points on the curve 4 y = |x2−4|at which tangents are parallel to x – axis, area)(4, 3) and (– 4, – 3)b)(0, 1) onlyc)(2, 0) and (– 2, 0)d)none of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The points on the curve 4 y = |x2−4|at which tangents are parallel to x – axis, area)(4, 3) and (– 4, – 3)b)(0, 1) onlyc)(2, 0) and (– 2, 0)d)none of theseCorrect answer is option 'B'. Can you explain this answer?.
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