How Do You Interpret The First Derivative (Single Variable Calculus)?
In single variable calculus, the first derivative measures the rate of change of the function. When the derivative is evaluated at a certain point, the numerical value of the first derivative can be interpreted as the slope of the tangent line at that point. If you are studying derivatives in calculus, here are some tips to help you understand and interpret the first derivative. Understand that the formal definition of a derivative of a function f(x) is the following limit: [f(x+h) – f(x)]/h as h goes to zero. The numerator of the limit is difference in y-values of the function, and the denominator is the difference in x-values. It is analogous to the formula for the slope of the line segment between two points (x1, y1) and (x2, y2), ie slope = (y2-y1)/(x2-x1). In this case, the two points are (x, f(x)) and (x+h, f(x+h)). This is why the derivative can be interpreted as a slope. Understand that there are several ways to write the first derivative. For example, if you have function deno
