Applications of Derivatives

Applications of Derivatives:

In this blog we are going to discuss about one of the most important concept application of derivatives along with Application of derivatives examples.

the derivative is a measure of how a function changes as its input changes. The process of measuring a derivative is called differentiation. The reverse process is antidifferentiation.

Derivatives is not a simple concept.It has a many applications.Using this applications we can solve different derivatives problems.

1. Rate of change of quantities
2. Errors and approximation
3. Rolle's and Lagrange's theorem
4. Maxima and minima functions
5. Increasing function and decreasing functions
6. Tangents and normal
7. Optimization
8. Graph shape.

Above mention all are application of derivatives.

Solve Application of derivatives Examples-

Solve and show that the function f(x) = (2x - sin x) is increasing for all x ε R.

Solution:

f(x) = (2x - sin x) ------ Given

Differentiate the function (2x - sin x) with respect to ' x ', we get

f '(x) = (2 - cos x) ≥ 0 for all x ε R.

Therefore, f '(x) ≥ 0 for all x ε R.

Hence, f(x) = (2x - sin x) is increasing for all x ε R

This is how we can solve application of derivatives problems.Above mention example is a very small part of application of derivatives example.

Next blog we will learn about something more about derivatives and related solved problems.