The slope of the tangent line to a curve measures the instantaneous rate of change of a curve. We can calculate it by finding the limit of the difference quotient or the difference quotient with incre...The slope of the tangent line to a curve measures the instantaneous rate of change of a curve. We can calculate it by finding the limit of the difference quotient or the difference quotient with increment h . The derivative of a function f(x) at a value a is found using either of the definitions for the slope of the tangent line. Velocity is the rate of change of position. As such, the velocity v(t) at time t is the derivative of the position s(t) at time t .
The instantaneous rate of change is the slope of the tangent line, which is the line that just touches the graph at the point of interest, and has the same rate of change (slope) as the function does ...The instantaneous rate of change is the slope of the tangent line, which is the line that just touches the graph at the point of interest, and has the same rate of change (slope) as the function does at the point. As the points we pick get closer and closer to the point (2,4) on the graph of \( y = x^2\), the slopes of the lines through the points and (2,4) are better approximations of the slope of the tangent line, and these slopes are getting closer and closer to 4.
