- #1
mcastillo356
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- TL;DR Summary
- Don't know if it is meaningless something said about a proof on extreme value existence
Hi, PF
"It is more difficult to draw the graph of a function whose domain has an endpoint at which the function fails to have an extreme value", states my textbook, "Calculus: A Complete Course"
A function with no max or min at an endpoint Let
Show that ##f## is continuous on ##[0,\infty)## and differentiable on ##(0, \infty)## but it has neither a local maximum nor a local minimun at the endpoint ##x=0##
I think the continuity and the differentiability are meaningless for the proof
"It is more difficult to draw the graph of a function whose domain has an endpoint at which the function fails to have an extreme value", states my textbook, "Calculus: A Complete Course"
A function with no max or min at an endpoint Let
##f(x)=\begin{cases}{x\sin{\left(\dfrac{1}{x}\right)}}&\text{si}& x>0\\0 & \text{si}& x=0\end{cases}## |
I think the continuity and the differentiability are meaningless for the proof