(a) State whether or not the function satisfies the hypotheses of the Mean Value Theorem on the given interval, and (b) if it does, find each value of c in the interval (a,b) that satisfies the equation f'(c)={f(b)-f(a)}/{b-a}

f(x)=|x-1| on [0,4]

Question

(a) State whether or not the function satisfies the hypotheses of the Mean Value Theorem on the given interval, and (b) if it does, find each value of c in the interval (a,b) that satisfies the equation f'(c)={f(b)-f(a)}/{b-a}

f(x)=|x-1| on [0,4]

anonymous · Answer

trick question
well not really a trick

anonymous · Answer

$$f(x)=|x-1|$$ is not differentiable at $x=1$ as it has a corner there

anonymous · Answer

so a big fat NO for this one

anonymous · Answer

I'm pretty sure I have to find the derivative first right? so it would be $$f'(x)=\frac{ (x-1) }{ \left| x-1 \right| }$$

anonymous · Answer

oh...well that should've been obvious...

anonymous · Answer

forget the derivative
it does not exist at 1

anonymous · Answer

also you are doing way way too much work

anonymous · Answer

Wow thanks for pointing that out

anonymous · Answer

the derivative is just 1 or -1, depending on whether $x>1$ or $x<1$
not sure how you found that derivative, but it is not really what you want
just two numbers is all

anonymous · Answer

alright well thanks

anonymous · Answer

yw