A differential question

A

acreech

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Find a and b such that f is differtiable everywhere


f(x)={2cos(7x) if x<0
{ax+b if x>=0



I have no idea how to do this problem so any help would be appreciated. Thanks
 
acreech said:
Find a and b such that f is differtiable everywhere


f(x)={2cos(7x) if x<0
{ax+b if x>=0



I have no idea how to do this problem so any help would be appreciated. Thanks
Click to expand...

At what x, you expect trouble here? Why?

What condition/s must f(x) meet to be differentiable?
 
I don't really understand the question myself which is part of the problem.

There is a similar question in the chapter questions of my book that at least has answers posted in the back. It reads as follows:

find a and b such that f is differentiable everywhere

f(x)={ax^3, x<=2
{x^2+b, x>2

The answers given are a=1/3 b=-4/3


I'm not sure how they arrived at this answer so I can't see how to relate it to the question I'm working on.
 
acreech said:
I don't really understand the question myself which is part of the problem.

There is a similar question in the chapter questions of my book that at least has answers posted in the back. It reads as follows:

find a and b such that f is differentiable everywhere

f(x)={ax^3, x<=2
{x^2+b, x>2

The answers given are a=1/3 b=-4/3


I'm not sure how they arrived at this answer so I can't see how to relate it to the question I'm working on.
Click to expand...

Please tell us:

What condition/s must f(x) meet to be differentiable everywhere?

If you don't know the answer - do a google search with keywords:

differentiability of a function

In particular study:

http://www.zweigmedia.com/RealWorld/cal ... diffb.html

Final advice: Make internet querry machines your friend - it will save you lot of time.
 
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