The slope is equal to the tangent of the inclination angle.

Inclination is the angle between the tangent of a point on the function image and the X axis. Each given point has its corresponding inclination, and the slope is the tangent of the inclination, that is, if the inclination is expressed as α, the slope is tanα.

The slope and inclination of every point on a straight line (linear function) are equal, but the slope and inclination of every point on a curve (such as quadratic function) are not necessarily equal. Meanwhile, the slope is the derivative of the original function.

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)

Analysis of the relationship between slope and inclination.

The inclination and slope of a straight line are the beginning of high school analytic geometry. It is one of the important concepts of analytic geometry, the geometric characteristics and algebraic representation of describing the inclination of a straight line, and the basis for studying straight lines and their geometric properties by coordinate method. We should not only understand the concept and get the formula, but also understand the algebraic process of geometric problems, and initially penetrate the basic thinking methods of analytic geometry. In order to master the knowledge about the inclination and slope of a straight line, here are some questions about the inclination and slope of a straight line.

The requirement of ordinary high school mathematics curriculum standard for the slope and inclination of a straight line is to understand the relationship between the slope and inclination of a straight line and calculate the slope of a straight line according to its inclination.