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Abstract
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In this paper, we describe the Mean Value Theorem (MVT) and Cauchy Mean Value Theorem (CMVT) when considering an Rn-1 dimensional hyperplane intersects an Rn-1 dimensional smooth surface in Rn. We demonstrate how we derive the the proofs of MVT and CMVT by applying techniques described in [Yang]. We further discuss how the theorems can be extended by replacing the hyperplane with another smooth surface. Next, we link MVT to problems of finding the extreme values for a smooth function subject to several constraints. We use technological tools to show how we can obtain the solutions that are guaranteed by our theories. Complete paper can be found at https://php.radford.edu/~ejmt/deliveryBoy.php?paper=eJMT_v6n1p1.
Reference.
[Yang] W.-C. Yang, .Revisit Mean Value, Cauchy Mean Value and Lagrange Remainder Theorems, Electronic Journal of Mathematics and Technology (eJMT), ISSN 1933-2823, Issue 2, Vol.1, June, 2007.
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