Differentiation is a method to compute the rate at which a dependent output
If
The simplest case is when
This formula is true because:
It follows that:
This gives an exact value for the slope of a straight line. If the function
Inflection Point
A point where the second derivative of a function changes sign is called an inflection point. At an inflection point, the second derivative may be zero, as in the case of the inflection point
![](../../../../../../../figures.boundless-cdn.com/17933/large/of-sliding-derivative-line.gif)
Derivative
At each point, the derivative of is the slope of a line that is tangent to the curve. The line is always tangent to the blue curve; its slope is the derivative. Note derivative is positive where a green line appears, negative where a red line appears, and zero where a black line appears.