1, solution

In advanced mathematics, the tangent of derivative is to find its derivative at a certain point, that is, the slope, and then get the tangent equation according to the coordinates of that point. In elementary mathematics, tangent is the slope of the tangent equation obtained by combining the discriminant of equation and quadratic equation when one variable is equal to 0.

2. Tangent form

In elementary mathematics, the curve is "appropriate", that is, the tangent line is tangent to the tangent point and does not intersect with the curve, while in advanced mathematics, the tangent line defined by the derivative can "cross the curve", that is, the tangent line is tangent to the tangent point and can cross the curve.

3. Tangent point

Elementary mathematics generally has only one tangent point, but advanced mathematics can have many or even countless tangent points.

Extended data:

Geometric and Algebraic Significance of Tangents

Geometrically, a tangent is a straight line that just touches a point on a curve. More precisely, when the tangent passes through a point on the curve (i.e. the tangent point), the direction of the tangent is the same as that of the point on the curve.

In plane geometry, a straight line with only one common intersection with a circle is called the tangent of the circle.

1, geometric meaning

P and Q are two adjacent points on curve C, and P is a fixed point. When point Q is infinitely close to point P along curve C, the limit position PT of secant PQ is called the tangent of curve C at point P, and point P is called the tangent point.

A straight line PN passing through the tangent point P and perpendicular to the tangent line PT is called the normal of the curve C at the point P (the idea of infinite approximation).

2. Algebraic significance

In advanced mathematics, if a function has a derivative somewhere, then the derivative here is the slope of the tangent line passing through it, and the straight line formed by this point and the slope is the tangent line of the function.

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