Application of Derivatives Class 12 Notes Chapter 6

What are Derivatives?

Derivatives are referred to the situation when a quantity p varies with respect to another quantity q, fulfilling a condition p =f (q) and dp/dq (or f ‘ (q)) represents the change of rate of p with respect to q and dp/dq where q =

Students can refer to the short notes and MCQ questions along with separate solution pdf of this chapter for quick revision from the links below:

• Application of Derivative Study Notes PDF
• Application of Derivative MCQ Practice Questions PDF
• Application of Derivative MCQ Practice Solutions PDF

CBSE Class 12 Maths Notes Chapter 6 Application of Derivatives – Related Links

• Applications of Derivatives – Basics
• Application Of Derivatives For Class 12
• Derivatives
• Important Questions for Class 12 Maths Chapter 6 – Applications of Derivatives

Chain Rule

Let us consider two variables, p and q, which vary with respect to the presence of another variable r, which means p = f(r) and q = g(r), then according to the chain rule,

Increasing and Decreasing Function

A Function p can be said to increase when:

• We can see an increase on an interval (a,b) if
  \(\begin{array}{l}x_{1}<x_{2}\end{array} \)
  in (a,b) =>
  \(\begin{array}{l}p(x_{1})<p(x_{2})\end{array} \)
  for all
  \(\begin{array}{l}x_{1}, x_{2}\epsilon (a,b)\end{array} \)

A function is said to be decreasing when:

• if
  \(\begin{array}{l}x_{1}<x_{2}\end{array} \)
  in (a,b) when:
  \(\begin{array}{l}x_{1}>x_{2}\end{array} \)
  for all
  \(\begin{array}{l}x_{1}, x_{2}\epsilon (a,b)\end{array} \)

Constant

The constant term in (a,b) if p(x)= q for all

Equation of Tangent

The equation of a tangent is given at a point

Critical point

The point q inside the domain of a function f at which f ‘ (q) =0 or f cannot be differentiable is referred to as the critical point of f.

Important Questions

1. Find out the value of m if line y=mx+1, which is a tangent to the curve
   \(\begin{array}{l}y^{2}=4x\end{array} \)
   .
2. For the curve
   \(\begin{array}{l}2y+x^{2}=3\end{array} \)
   is?

3. A semicircular opening is surmounted by a window which is in the form of a rectangle. The total perimeter of the window is 50 m. Find the dimensions of the window to admit maximum light through the whole opening.

4. A point on the hypotenuse of a triangle is at a distance p and q from the sides of the triangle.

5. For what values of a the function f given by f(x) =
   \(\begin{array}{l}x^{2}\end{array} \)
   + ax + 1 is increasing On [1, 2]?

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