Differentiation

[TheNextOne]

Let f(x)= (9 - 2x) if x >4
1/(5 - x) if x is less than or equla to 4.

Use the definition ofa derivative to determine whether f is differentiable at x=4.

My solution-

I know you have to differntiate the two functions and show that they are not equal and thus not differentiable. But the solution I have has a negative sign infront of the second function. I do not understand where that negative sign came from.
When I worked the problem out I fot F'(x)= 1 for the second function and f'(x)= -2 for the first function. The solution has -1 and -2. Where did I go wrong?

 

[stapel]

When I worked the problem out I got.... Where did I go wrong?

In order for the tutors to be able to check your work, you will need to post your work.

Please reply showing all the steps you did.

Thank you.

Eliz.

 

[soroban]

Hello, TheNextOne!

Let \(\displaystyle \:f(x)\:=\:\begin{array}{cc}9\,-\,2x\:\text{ if }x\,>\,4\\ \frac{1}{5\,-\,x}\:\text{ if }x\,\leq\,4\end{array}\)

Use the definition of a derivative to determine whether \(\displaystyle f\) is differentiable at \(\displaystyle x=4\)

My solution:
I got \(\displaystyle f'(4)\,=\,1\) for the second function
\(\displaystyle \;\;\)and \(\displaystyle f'(4)\,=\, -2\) for the first function.
The solution has -1 and -2. \(\displaystyle \;\) . . . They are wrong!

You did nothing wrong . . . good work!