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The slope of the tangent to the curve y = x2 –x at the point, where the line y = 2 cuts the curve in the Ist quadrant, is
  • a)
    2
  • b)
    3
  • c)
    –3
  • d)
    none of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The slope of the tangent to the curve y = x2 –x at the point, wh...
 The point at which line y=2 cut the curve can be found out by
       2=x^2-x
       x^2-x-2=0
     on solving we will get, 
     x=-1,2
 since, the point is in first quadrant, So, x=2

Thus, point is (2,2).
Slope of the curve can be found out by differentiating the the equation of curve with respect to the x.
  dy/dx= 2x-1
Now, put the value of x
   dy/dx=2(2)-1=4-1=3
Therefore, the slope is 3.

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Most Upvoted Answer
The slope of the tangent to the curve y = x2 –x at the point, wh...
Finding the Point of Intersection

To find the point of intersection between the curve y = x^2 and the line y = 2, we need to substitute y = 2 in the equation of the curve and solve for x.

2 = x^2

Taking the square root of both sides, we get:

x = ±√2

Since the line y = 2 cuts the curve in the first quadrant, we take the positive root:

x = √2

Finding the Slope of the Tangent

To find the slope of the tangent to the curve at the point (√2, 2), we need to take the derivative of the curve with respect to x and evaluate it at x = √2.

y = x^2

Taking the derivative with respect to x, we get:

dy/dx = 2x

Evaluating at x = √2, we get:

dy/dx = 2√2

Therefore, the slope of the tangent to the curve at the point (√2, 2) is 2√2.

Simplifying, we get:

2√2 = 2(1.414) = 2.828

Therefore, the correct answer is option B, 3 (rounded to the nearest integer).
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The slope of the tangent to the curve y = x2 –x at the point, where the line y = 2 cuts the curve in the Ist quadrant, isa)2b)3c)–3d)none of theseCorrect answer is option 'B'. Can you explain this answer?
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