Question

The equation of the tangent line to a level curve is determined by which of the following?

a) The slope of the curve
b) The derivative of the curve
c) The intersection points of the curve
d) The area under the curve

Answer 1

The equation of the tangent line to a level curve is determined by the derivative of the curve, which gives the slope of the tangent line at a specific point.

Step-by-step explanation:

The equation of the tangent line to a level curve is determined by the derivative of the curve. To find the tangent line at a specific point on the curve, one must compute the slope at that point, which is done by taking the derivative. The slope at a given point is equal to the slope of the tangent line at that point.

For instance, if a point Q is at t = 25 s on a graph, the tangent line to the curve at Q can be found by calculating the derivative at t = 25 s. This gives the slope of the tangent which, combined with the point of tangency, allows us to express the tangent line equation.

Steps to Find the Tangent Line

1. Compute the derivative of the curve to find the slope function.
2. Evaluate the slope function at the point of interest (e.g., t = 25 s) to find the slope of the tangent line.
3. Use the slope and the coordinates of the point to write the equation of the tangent line.