Define Differentiable In Calculus Math

That sounds a bit like a dictionary definition doesn t it.

Define differentiable in calculus math. In mathematics differential calculus is used to find the rate of change of a quantity with respect to other. In traditional approaches to calculus the differentials e g. Differentiable functions are nice smooth curvy animals. They have no gaps or pointy bits.

In case of finding a function is increasing or decreasing functions in a graph. In calculus a branch of mathematics a differentiable function of one real variable is a function whose derivative exists at each point in its domain in other words the graph of a differentiable function has a non vertical tangent line at each interior point in its domain. But if you explore this idea a little further you ll find that it tells you exactly what differentiable means. A differentiable function is one you can differentiate.

The differentiable function is smooth the function is locally well approximated as a linear function at each interior. Completely accurate but not very helpful. This device cannot display java animations. The total differential is its generalization for functions of multiple variables.

To find the approximate value of small change in a quantity. To be differentiable at a certain point the function must first of all be defined there. In calculus the differential represents a change in the linearization of a function. So it is not differentiable.

To find the maximum and minimum value of a curve. As we head towards x 0 the function moves up and down faster and faster so we cannot find a value it is heading towards. Dx dy dt etc are interpreted as infinitesimals there are several methods of defining infinitesimals rigorously but it is sufficient to say.