If f(x) = x^3+x^2+x+1, find a number "c" that satisfies the conclusion of the mean value theorem for the inter?

If f(x) = x^3+x^2+x+1, find a number "c" that satisfies the conclusion of the mean value theorem for the interval [1, 3]If f(x) = x^3+x^2+x+1, find a number "c" that satisfies the conclusion of the mean value theorem for the inter?f(x) = x^3 + x^2 + x + 1 is the extended version of the factorial set ( x^2 + 1 ) ( x + 1 )



If you plug in the given interval [1,3] (where 1 is the x in the first set, and 3 is the x in the second one), you get:



( 3^2 + 1) ( 3 + 1)



( 9 + 1) ( 3 + 1)



10 * 4 = 40



So I think that the answer your teacher is looking for is 40. However, it's been a while since I did this type of math, so there might be another part of the problem that I'm not picking up on.



[That being said, if you solve the first equation f(x) = x^3+x^2+x+1 by plugging in 3 for each x, the answer is also 40. Plug in 1 instead, and the answer you get is 4... which, since 0 can be tricky in math, might mean that the 'mean' answer for both ends up being 4. Hope this part wasn't too confusing...]



Hope this helps you understand the question better (and/or eventually get to the right answer if I did it wrong)!If f(x) = x^3+x^2+x+1, find a number "c" that satisfies the conclusion of the mean value theorem for the inter?Not clear question!!

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