Now that we know how to find the derivative of a function, it is important to know that we can take the derivative more than once.
The first derivative, as we know, gives us the gradient (slope of the tangent line) of a function at any given point (x) on the curve—in other words, whether the curve's altitude (that is, y or f(x)) is increasing or decreasing. A positive slope tells us f(x) is increasing as x increases and a negative slope tells us f(x) is decreasing as x increases, and a slope of 0 tells us nothing about the curve's direction, other than that it is likely at a turning point (local minimum or local maximum). This can be written as follows:
- If , then f(x) is increasing at x = t.
- If , then f(x) ...
