Afunctionthat has a continuous derivative isdifferentiable; It’s derivative is acontinuous function. How do I know if I have a continuous derivative? As the definition of a continuous derivative includes the fact that the derivative must be a continuous function, you’ll have tocheck for contin...
In mathematics, the term derivative refers to the rate of change of a function with respect to a variable. Derivatives play an important role in solving problems in calculus and differential equations including finding local extrema, solving optimization problems, finding inflection points, and describi...
The derivative must exist for every point in the domain, otherwise the function is not differentiable. This might happen when you have a hole in the graph: if there’s a hole, there’s no slope (there’s a dropoff!).See: Differentiable vs. Non Differentiable Functions....
Mathematically, you find them by looking at thederivative. At an extreme point, where there is a direction change, the derivative of the function is zero. Note: thederivativeis the slope of thetangent line. In the above graph, the tangent line is horizontal, so it has a slope (derivative...