Hey folks, I haven't the foggiest idea how to start this problem. A tip or push in the right direction or link to a resource that explains these types of problems would be just great.
I've only done problems with the Mean Value Theorem of the form "Find 2 roots of and comfirm that at some point between those roots.a. Use the Mean Value Theorem to show that for ,
.
b. Use part (a), above, to conclude that for ,
Even just a hint or link would be great, thanks guys.
So if I'm understanding this correctly, we are using the mean value theorem (Which states that there is a in between and that makes that inequality valid), to show that
And then we algebraically manipulate this into the answer?
I'm sorry for the probably extremely basic questions, I'm terrible with the theorems and proofs and need serious work on them.
But also, given the inequality in the original equation, shouldn't our derived equality be of the form ? How did those values get switched around?
OH! I see!
So the Mean Value Theorem states where in our case, and and , thus .
That's where came from, because
So we substitute this into the inequality you gave me , axe off the very left hand side of the equation and solve for
which gives us
Which is what we are trying to show is valid under the condition
Right?