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函数切线问题是高考热点之一,导数与函数的切线有缘,因为f’(x_0)的几何意义是曲线y=f(x)在点(x_0,f(x_0))处的切线斜率。因此,利用导数求解函数问题,是新课标高考重点考查内容。在这类问题中,导数所肩负的任务是求切线的斜率,考查函数的思想方法和解析几何的基本思想方法,真正体现出函数、导数既是研究的对象又是研究的工具。下面举例说明。一、求曲线的切线方程例1(2012年广东卷·理12)曲线y=x~3-x+3在点(1,3)处的切线方程为____。
The function tangent problem is one of the entrance exam hotspots. The derivative is tangent to the function because the geometric meaning of f ’(x_0) is the tangent slope of the curve y = f (x) at the point (x_0, f (x_0)). Therefore, the use of derivatives to solve the problem of function, is the focus of the new curriculum exam entrance exam content. In these kinds of problems, the task of the derivative is to find the slope of the tangent, the method of thinking and the method of analyzing the geometry, and the derivative of the function is the object of study and the tool of research. Here’s an example. First, find the curve of the tangent equation Example 1 (2012 Volume 12) curve y = x ~ 3-x + 3 at the point (1,3) at the tangent equation ____.