What is the tangent line to the curve at the given point?

Thread starter fk378
Start date Oct 16, 2007
Tags

Curve Line Tangent Tangent line

In summary, a tangent line to a curve is a straight line that touches the curve at only one point and represents the instantaneous rate of change or slope of the curve at that specific point. The slope of a tangent line can be calculated by taking the derivative of the curve at the given point. It represents the instantaneous rate of change of the curve and can be used to determine the direction and steepness of the curve. The significance of a tangent line lies in its ability to help us understand the behavior of the curve at a specific point and make predictions about its future values. A tangent line can also be horizontal if the slope of the curve is equal to 0 at that point.

Oct 16, 2007

fk378

Homework Statement

Find the tangent line to the curve y^2 (y^2 - 4) = x^2 (x^2 -5) at the point (0,-2).

Homework Equations

y-y1=m(x-x1)

The Attempt at a Solution

I d/dx-ed both sides and was left with dy/dx=0
so
y=-2
Does that seem right?

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Oct 16, 2007

atqamar

Yup that's correct!

FAQ: What is the tangent line to the curve at the given point?

What is a tangent line to a curve?

A tangent line to a curve is a straight line that touches the curve at only one point, known as the point of tangency. It represents the instantaneous rate of change or slope of the curve at that specific point.

How is a tangent line to a curve calculated?

The slope of a tangent line to a curve can be found by taking the derivative of the curve at the given point. This derivative represents the rate of change of the curve at that point, which is also the slope of the tangent line.

What does the slope of the tangent line to a curve represent?

The slope of the tangent line to a curve represents the instantaneous rate of change of the curve at that specific point. It shows how much the curve is changing at that point, and can be used to determine the direction and steepness of the curve.

What is the significance of a tangent line to a curve?

The tangent line to a curve is significant because it helps us understand the behavior of the curve at a specific point. It can also be used to approximate the curve and make predictions about its future values.

Can a tangent line to a curve be horizontal?

Yes, a tangent line to a curve can be horizontal if the slope of the curve at that point is equal to 0. This means that the curve is neither increasing nor decreasing at that specific point.