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is the slope of a secant line to the curve. For a line, the secant between any two points is the line itself, but this is not the case for any other type of curve. For example, the slope of the secant intersecting y = x 2 at (0,0) and (3,9) is 3. (The slope of the tangent at x = 3 ⁄ 2 is also 3 − a consequence of the mean value theorem.)
The linear portion of the curve is the elastic region, and the slope of this region is the modulus of elasticity or Young's modulus. Plastic flow initiates at the upper yield point and continues at the lower yield point. The appearance of the upper yield point is associated with the pinning of dislocations in the system.
The slope of the yield curve is one of the most powerful predictors of future economic growth, inflation, and recessions. [12] [13] One measure of the yield curve slope (i.e. the difference between 10-year Treasury bond rate and the 3-month Treasury bond rate) is included in the Financial Stress Index published by the St. Louis Fed. [14]
l = slope length α = angle of inclination. The grade (US) or gradient (UK) (also called stepth, slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line is either the elevation angle of that surface to the horizontal or its tangent. It is a special case of the slope, where zero indicates horizontality. A ...
Placing position on the y-axis and time on the x-axis, the slope of the curve is given by: = =. Here is the position of the object, and is the time. Therefore, the slope of the curve gives the change in position divided by the change in time, which is the definition of the average velocity for that interval of time on the graph.
Curve fitting [1] [2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [3] possibly subject to constraints. [ 4 ] [ 5 ] Curve fitting can involve either interpolation , [ 6 ] [ 7 ] where an exact fit to the data is required, or smoothing , [ 8 ] [ 9 ] in which a "smooth ...
A curve point (,) is regular if the first partial derivatives (,) and (,) are not both equal to 0.. The equation of the tangent line at a regular point (,) is (,) + (,) =,so the slope of the tangent line, and hence the slope of the curve at that point, is
The slope field can be defined for the following type of differential equations ′ = (,), which can be interpreted geometrically as giving the slope of the tangent to the graph of the differential equation's solution (integral curve) at each point (x, y) as a function of the point coordinates.