suppose f(x)= sqrt of 1+3x, x>or equal to 5

k(x^2-5), x<5

for what value of k is continuous? For what value of k is f differentiable?

not even sure where to start i think i am on dealing with the second equation in this piecewise function

Printable View

- October 15th 2008, 07:27 AMvinson24the derivative function
suppose f(x)= sqrt of 1+3x, x>or equal to 5

k(x^2-5), x<5

for what value of k is continuous? For what value of k is f differentiable?

not even sure where to start i think i am on dealing with the second equation in this piecewise function - October 15th 2008, 09:17 AMChris L T521
A function is continuous at a point when exists. This means that

Quote:

For what value of k is f differentiable?

not even sure where to start i think i am on dealing with the second equation in this piecewise function

Note that you may not get the same k value for the continuity and differentiability cases...

Can you try these now and see what you get?

--Chris - October 15th 2008, 09:36 AMvinson24
im still not seeing it

- October 15th 2008, 10:38 AMvinson24
i know f is continuous if k=1/5 and f is differentianle if k=3/80 but not seeing how to get there

- October 15th 2008, 02:00 PMChris L T521
Let's find

Now find

The function is continuous when

Does this bit make sense?

Quote:

For what value of k is f differentiable?

not even sure where to start i think i am on dealing with the second equation in this piecewise function

Now, let's look at the derivative of the function for :

In order for this function to be differentiable at , both of these derivatives must have the same value at :

This implies that

Does this make sense?

--Chris