Question

Find the cordinant of the point on the curve y=x-4/x.where the tangent are parallel to the line y=2x

Answer 1

Answer:

(2, 0) and (-2, 0).

Step-by-step explanation:

Since tangent is to be parallel to the line y = 2 x, the slope of the tangent should be equal to 2.

Given  curve  y = x - 4/x.

Tangent slope = y' = dy/dx = 2.

  y' = 1 + 4/x² = 2  

 => 4/x² = 1

=> x = +2 or -2.

y = 0 for these points.

Points are : (2,0) and (-2,0).

Answer 2

The slope of a tangent drawn at any point (a, f(a)) to a curve described by y = f(x) is given by the value of f'(a).

For the curve y = x - 3x^2 + 2, the derivative y' = 1 - 6x. If a line is parallel to the x-axis, the slope of the line is 0.

To determine the point required in the problem solve y' = 0 for x.

1 - 6x = 0

=> x = 1/6

y = 1/6 - 3*(1/36) + 2 = 25/12

At the point the tangent to the curve y = x - 3x^2 + 2 is parallel to the x-axis.

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