Calculus/Continuity

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Expert: - 5/31/2008


Question
Dear Sir,
I am megahana and undergraduate student. I am not understanding that,
1) what is exact difference between continuous and differentiability? 2)
some times, some functions are continuous but not differentiable. how?
I am fully confused in this part. please explain with a suitable
example.
Thanking you,
yours faithfully,
Meghna

Answer

abs(x)
Questioner:   MEGHNA NAIDU
Category:  Calculus
Private:  No
 
Subject:  continous
Question:  Dear Sir,
.........................
Hi, Megahana or Meghna, however you like to spell it.


I am megahana and undergraduate student. I am not understanding that,
1) what is exact difference between continuous and differentiability?

>> Check the definitions.  They say different things.  As a general rule,

f(x) is continuous if its graph has no break.
f(x) is differentiable if its graph is smooth.(of course, if it has a break, it cannot be smooth)

2)some times, some functions are continuous but not differentiable. how?

>> You bet they are.  Obvious example:

f(x) = absolute value of x.

It's continuous at x = 0, but not smooth there.
(See attached graph.)

Now go back and really study those definitions.  Make sure you know what the vocabulary means.

Paul Klarreich

Expertise

All topics in first-year calculus including infinite series, max-min and related rate problems. Also trigonometry and complex numbers, theory of equations, exponential and logarithmic functions. I can also try (but not guarantee) to answer questions on Analysis -- sequences, limits, continuity.

Experience

I taught all mathematics subjects from elementary algebra to differential equations at a two-year college in New York City for 25 years.

Education/Credentials
(See above.)

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