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
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
A function is continuous at a point when exists. This means that
It is differentiable at that point if the derivatives of the first and second terms in the piecewise function are the same at that point.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
Let's find
Now find
The function is continuous when
Does this bit make sense?
Let's look at the derivative of the function for :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