Question

Find the point on the curve Y is equal to x cube minus 11 x + 5 at which the tangent is Y is equal to x minus 11

Answer 1

Step-by-step explanation:

Let the required point of contact be (x, y)

Given: The equation of the curve is y=x

3

−11x+5

The equation of the tangent to the circle as y=x−11 (which is of the form y = mx + c)

Therefore, Slope of the tangent = 1

Now, the slope of the tangent to the given circle at the point (x, y) is given by

dx

dy

=3x

2

−11

Then, we have:

3x

2

−11=1

3x

2

=12

x

2

=4

x=±2

Whenx=2,y=(2)

3

−11(2)+5=8−22+5=−9.

When x=−2,y=(−2)

3

−11(−2)+5=−8+22+5=19.

So, the required point are (2,−9) and (−2,19)

But (2, -19) does not satisfy the line y = x - 11

Therefore, (2, -9) is required point of curve at which tangent is y=x−11.

Answer 2

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