Here, we provided to Application Of Derivatives Hand Written Note. There are various applications of derivatives not only in maths and real life but also in other fields like science, engineering, physics, etc. In previous classes, you must have learned to find the derivative of different functions, like, trigonometric functions, implicit functions, logarithm functions, etc. Free download PDF Application Of Derivatives Hand Written Note.

The concept of derivatives has been used on a small scale and large scale. The concept of derivatives used in many ways such as change of temperature or rate of change of shapes and sizes of an object depending on the conditions etc., Free download PDF Application Of Derivatives Hand Written Note.

The derivative is defined as the rate of change of one quantity with respect to another. In terms of functions, the rate of change of function is defined as dy/dx = f(x) = y’. The ratio of dy/dx is used as one of the applications of derivatives in real life and various aspects. Free download PDF Application Of Derivatives Hand Written Note.

**Derivatives have various important applications in Mathematics such as:**

- Rate of Change of a Quantity
- Increasing and Decreasing Functions
- Tangent and Normal to a Curve
- Minimum and Maximum Values
- Newton’s Method
- Linear Approximations

**Applications of Derivatives in Maths:**

The derivative is defined as the rate of change of one quantity with respect to another. In terms of functions, the rate of change of function is defined as dy/dx = f(x) = y’. The ratio of dy/dx is used as one of the applications of derivatives in real life and various aspects. Free download PDF Application Of Derivatives Hand Written Note.

The concept of derivatives has been used on a small scale and large scale. The concept of derivatives used in many ways such as change of temperature or rate of change of shapes and sizes of an object depending on the conditions etc., Free download PDF Application Of Derivatives Hand Written Note.

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**BOOK NAME** – APPLICATION OF DERIVATIVES HAND WRITTEN NOTE

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**Rate of Change of a Quantity:**

This is the general and most important application of derivative. For example, to check the rate of change of the volume of a cube with respect to its decreasing sides, we can use the derivative form as dy/dx. Where dy represents the rate of change of volume of cube and dx represents the change of sides of the cube. Free download PDF Application Of Derivatives Hand Written Note.

**Increasing and Decreasing Functions:**

To find that a given function is increasing or decreasing or constant, say in a graph, we use derivatives. If f is a function which is continuous in [p, q] and differentiable in the open interval (p, q), then, Free download PDF Application Of Derivatives Hand Written Note.

- f is increasing at [p, q] if f'(x) > 0 for each x ∈ (p, q)
- f is decreasing at [p, q] if f'(x) < 0 for each x ∈ (p, q)
- f is constant function in [p, q], if f'(x)=0 for each x ∈ (p, q)

**Tangent and Normal To a Curve:**

Tangent is the line that touches the curve at a point and doesn’t cross it whereas normal is the perpendicular to that tangent. Free download PDF Application Of Derivatives Hand Written Note.

**Maxima and Minima:**

To calculate the highest and lowest point of the curve in a graph or to know its turning point, the derivative function is used.

- When x = a, if f(x) ≤ f(a) for every x in the domain, then f(x) has an Absolute Maximum value, and the point a is the point of the maximum value of f.
- When x = a, if f(x) ≤ f(a) for every x in some open interval (p, q) then f(x) has a Relative Maximum value.
- When x= a, if f(x) ≥ f(a) for every x in the domain then f(x) has an Absolute Minimum value, and the point a is the point of the minimum value of f.
- When x = a, if f(x) ≥ f(a) for every x in some open interval (p, q) then f(x) has a Relative Minimum value.

**Monotonicity:**

- Functions are said to be monotonic if they are either increasing or decreasing in their entire domain.
- Functions which are increasing and decreasing in their domain are said to be non-monotonic

**Approximation or Finding Approximate Value:**

To find a very small change or variation of a quantity, we can use derivatives to give the approximate value of it. The approximate value is represented by delta △.

**Point of Inflection:**

For continuous function f(x), if f'(x0) = 0 or f’”(x0) does not exist at points where f'(x0) exists and if f”(x) changes sign when passing through x = x0 then x0 is called the point of inflection.

**Application of Derivatives in Real Life:**

- To calculate the profit and loss in business using graphs.
- To check the temperature variation.
- To determine the speed or distance covered such as miles per hour, kilometer per hour, etc.
- Derivatives are used to derive many equations in Physics.
- In the study of Seismology like to find the range of magnitudes of the earthquake.

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