Differential calculus is the study of rates of change of functions using limits and derivatives. The derivative of a function represents the rate of change of the output variable with respect to the input variable or slope at a point. A function is continuous if it has no holes or jumps at any point in its domain. The tangent line approximates the curve at a point, while the normal line is perpendicular to the tangent line. Maxima and minima refer to local extremes where the function reaches a maximum or minimum value. Derivatives can also be used to determine rates of change for a variety of applications.

1. Differential
calculusBy-Shubham
BCA 2C
A1004816146
TO:-MR. PREAM KUMAR

2. Index
Introduction
Differentiation and the Derivative
Limit and continuity
Tangent and normal
Maxima and minima
Rate

3. Introduction
Differential calculus is the study of rates of
change of functions, using the tools
of limits and derivatives.

4. Differentiation and the
Derivative
Differentiation is the algebraic method of
finding the derivative for a function at any point
The derivative of a function is rate of change
of Y axis with X(or slop at a point)

5. Limit
In mathematics, a limit is the value that a
function "approaches" as the input or index
approaches some value

6. Continuity
A function is then continuous if it has no holes
or jumps: that is, if it is continuous at every point
of its domain

7. Tangent and normal
 A straight line or plane that touches a curve or
curved surface at a point, but if extended
does not cross it at that point
Let f(x) is function
Differentiate it m=f’(x) where m is slope
Put value of x( say a)
Find tangent eqn by y-y1 =m(x-x1)
And normal by y-y1 =-1/m(x-x1)

8. Maxima and minima
 Places where they reach a minimum or
maximum value.
It may not be the minimum or maximum for
the whole function, but locally it is.

9. Rate
 Rate or speed of change of function