Data expansion:
1, the definition of slope
Slope, also known as "angle coefficient", indicates the inclination of a straight line relative to the abscissa axis in a plane rectangular coordinate system.
The tangent value tgα of the inclination angle α of a straight line with respect to the X axis is called the "slope" of the straight line, which is denoted as k, and k=tgα. It is stipulated that the slope of the straight line parallel to the X axis is zero, and the slope of the straight line parallel to the Y axis does not exist. For a straight line passing through two known points (x 1, y 1) and (x2, y2), if x 1≠x2, the slope of the straight line is k = (y1-y2)/(x/kloc-0).
Slope is a mathematical and geometric term, which can be expressed by the ratio of the difference between the ordinate and abscissa of two points, that is, k=tanα or k = Δ y/Δ x. If the straight line is perpendicular to the X axis, the tangent of the right angle is tan90, so the slope of the straight line is infinite.
2. Curve slope
The slope of a point on the curve reflects the changing speed of the variable of the curve at that point.
The trend of the curve can still be described by the slope of the tangent of a point on the curve, which is the derivative. The geometric meaning of derivative is the tangent slope of function curve at this point.
F'(x)>0, the function increases monotonically in this interval, and the curve shows an upward trend; f '(x)& lt； 0, the function monotonically decreases in this interval, and the curve shows a downward trend.
In (a, b) f'' (x)
3. Slope formula
When the slope of the straight line L exists, for the linear function y=kx+b (oblique section), k is the slope of the function image. When x=0, y = b.
When the slope of a straight line exists, the point inclination y2-y 1=k(x2-x 1),
When the straight line L has a non-zero intercept on two coordinate axes, there is an intercept formula x/a+y/b= 1.
For any point on any function, its slope is equal to the angle formed by its tangent and the positive direction of X axis, that is, k=tanQ.
The slope of curve y=f(x) at point (x 1, f(x 1)) is the derivative of function f(x) at point x 1.