Explore BrainMass
Share

# problems regarding differentiability and function operation

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

Please provide detailed solution:

What can you say about the differentiability of fg at x = c in each of the following cases? (Here the function fg is defined by fg(x) = f(x)g(x)).
(a) f is differentiable at c, but g is not.
(b) f is not differentiable at c, and neither is g.
(c) both f and g are differentiable at c.

© BrainMass Inc. brainmass.com December 20, 2018, 8:49 am ad1c9bdddf
https://brainmass.com/math/graphs-and-functions/problems-regarding-differentiability-function-operation-460525

#### Solution Preview

Hi there,

Thanks for letting me work on your questions. When c condition is met, (fg(x))'=f(x)'g(x)=f(x)g(x)'. so fg(x) is differentiable.
However, for condition a and b, the answer is not conclusive.
For ...

#### Solution Summary

This solution provides some explanation for differentiability and function operation.

\$2.19