Do you use the chair rule?Where on the curve does the tangent line have slope 1/3?
A perpendicular tangent line is a line that intersects a curve at a single point and forms a right angle with the curve at that point. This line represents the direction of the steepest slope at that point on the curve.
To determine the equation of a perpendicular tangent line, you need to first find the slope of the tangent line at the point of intersection with the curve. Then, you can use the negative reciprocal of the tangent line's slope to find the slope of the perpendicular line. Finally, you can use the point-slope formula to find the equation of the perpendicular tangent line.
The point-slope formula is a method for finding the equation of a line that passes through a given point and has a given slope. It can be written as: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the given slope.
Yes, a curve can have more than one perpendicular tangent line. This can occur when the curve has a point of inflection or a cusp, where the slope of the curve changes suddenly. In these cases, there can be multiple points where the curve intersects a line at a right angle.
Determining a perpendicular tangent line is useful in science because it allows us to find the direction of the steepest slope at a particular point on a curve. This can be helpful in analyzing the behavior of natural phenomena, such as the rate of change of a chemical reaction or the velocity of an object in motion. It also allows us to calculate the instantaneous rate of change, which is important in fields such as physics and biology.