synergix said:the relationship between the the slope of the tangent line and the slope of the normal line is that the tangent will be the inverse negative of the slope of the normal line.
so slope of the normal line= -1(-2-1)
1/2sqrt(x-1) = m = 1/2
sqrt(x-1) = 1
x = 2
Dick said:What you did is find the normal slope to the line and equate it to the tangent direction of the curve. That's sort of backwards, but if you understand why that works, it's ok with me.
A point of normal line is a point on a curve or surface where the tangent line is perpendicular to the normal line.
To find the point of normal line, you need to first find the slope of the tangent line at that point. Then, take the negative reciprocal of that slope to find the slope of the normal line. Finally, use the point-slope formula to find the equation of the normal line passing through the given point.
Points of normal line have many applications in science, especially in fields such as physics and engineering. They are used to determine the direction of motion or force acting on an object, and also to find the rate of change of a function at a specific point.
Yes, a curve can have multiple points of normal line. This happens when the curve changes direction or curvature at different points, causing the tangent line to be perpendicular to the curve at those points.
Points of normal line and points of inflection are related in that they both occur at points where the curvature of a curve changes. However, a point of normal line is where the tangent line is perpendicular to the curve, while a point of inflection is where the concavity of the curve changes from concave up to concave down or vice versa.