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2. Verify that the function f (x) = x x2 satisfies the hypotheses of the Mean Value Theorem on the interval [-1,2]:Find all numbers € that satisfy the conclus...

Question

2. Verify that the function f (x) = x x2 satisfies the hypotheses of the Mean Value Theorem on the interval [-1,2]:Find all numbers € that satisfy the conclusion of the Mean Value Theorem

2. Verify that the function f (x) = x x2 satisfies the hypotheses of the Mean Value Theorem on the interval [-1,2]: Find all numbers € that satisfy the conclusion of the Mean Value Theorem



Answers

II-14 Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. Then find all numbers c that satisfy the conclusion of the Mean Value Theorem.

$f(x)=\frac{x}{x+2},[1,4]$

Really going to solve problem number nine here. The given function f affects equal to do it to square minus three X plus more. It's a poor longer function. It is always differential and continues and mean Military is applicable, so differentiate ffx. If that is, execute toe for X minus three the street. Okay, so we have to find f D I C after I seek or two f off to minus fo zero developed by do minus settle. So I have this C equal toe two into two square minus three into two. Let's look minus to Indo zero square, minus three in 20 plus alarm. Do it by to so here if they see equal toe eight minus six plus one minus one developed by two. So it's like for C minus three equal to one for C equal to four. Seiko to one. Thank you

One day we're going to start. Call the number 10 here. The human function F of X equal toe excuse minus three X plus two. It's a polo malfunction. It is continuous and differential for our X then f d I C equal toe f off B minus F off a divided by B minus A with physical toe have died c equal toe for minus their all the world by tu minus minus two, which is equal to one after executive three X squared minus tree FBI Sex equals one three X squared minus three equals one X squared record four by three Sequel toe plus or minus 23 by three. Thank you.

We have a function x squared on the interval from 1-2. This function is continuous On that closed interval from 1-2 because it's polynomial equation And it's also differential on the open interval from 1-2. Again, because the derivative uh for polynomial always exist under the mean value theorem. The derivative at the X value of C should equal the average rate of change F of b minus F of a over b minus a. The derivative of the function and access to acts so the derivative at CS to see The function will be the functional annexes two is 4. The function at x equals one is 1 And that's all over B -A Tu -1. So we have to see equals 3/1 or three in dividing by two gives us three halves. That is in the interval. So that's where the mean value theorem, except

Today we are going to solve company. About 11 here ffx equal to no, that's so. It is different. Trouble and containers for all X greater than zero hence mean by the term is applicable on the given interval. If they execute toe one by x. So have nice sequel to F for four minus F off one different by four minus one. Have bicycle toe Ellen Fork minus Ln one Divided by three Ln one equal to zero f d I. C e called toe island for by three one by C equal to I learned four by three c equal to three by look for thank you.


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