4.4 Some Counter Examples

f (x) = x + x1 " x
ÎR is continuous at
x = 0 but not derivable at x = 0

f (x) = 0, if x £
0
= x, if x > 0 is continuous at x = 0 but not derivable
at x = 0

f (x) =
is continuous over its entire domain of real numbers, but its
derivative does not exist at x = 0.

f (x) = x+2 is continuous over the entire
domain of real numbers but is not derivable at x = 2
* THUS  Differentiability Þ continuity.
But continuity does not imply differentiability.

Index
4. 1 Derivability
At A Point
4. 2 Derivability In An Interval
4. 3 Derivability And Continuity Of A Function
At A Point
4. 4 Some Counter Examples
4. 5 Interpretation Of Derivatives
4. 6 Theorems On Derivatives (differentiation
Rules)
4. 7 Derivatives Of Standard Functions
4. 8 Derivative Of A Composite Function
4. 9 Differentiation Of Implicit Functions
4.10 Derivative Of An Inverse Function
4.11 Derivatives Of Inverse Trigonometric
Functions
4.12 Derivatives Of Exponential & Logarithmic
Functions
4.13 Logarithmic Differentiation
4.14 Derivatives Of Functions In Parametric
Form
4.15 Higher order Derivatives
Chapter
5
