How To: Find the equation of a tangent line

This is the video about how to find the equation of a tangent line. As you may recall, a line which is tangent to a curve at a point a, must have the same slope as the curve. Therefore, the slope of the tangent is m = lim f(a + h) - f(a) h-->0 h Since the slope equation of the tangent line is exactly the same as the derivative definition, an easier way to find the tangent line is to differentiate using the rules on the function f. For example, Find the slope of a line tangent to the function f(x) = x2 + 1. f '(x) = 2x The slope of the tangent line for all points on the graph is 2x. To find the slope and equation of a line tangent to a certain point, you must: First find the slope of the function by differentiation. Find the equation of the tangent line for the function f(x) = x2 + 1 at point (3,10). Find the slope of the function by differentiation f '(x) = 2x