Suppose that we approximate f ?( x ) by the 4th degree Taylor polynomial T 4 ( x

Question

Suppose that we approximate f?(x) by the 4th degree Taylor polynomial T4(x) centered at a = 1. Taylor's inequaltiy gives an estimate for the error involved in this approximation.

Find the smallest possible value of the constant M? referred to in Taylor's Inequality.

Suppose that we approximate f?(x) by the 4th degree Taylor polynomial T4(x) centered at a = 1. Taylor's inequaltiy gives an estimate for the error involved in this approximation.

Find the smallest possible value of the constant M? referred to in Taylor's Inequality.

I got -720*(5/8)^7 using Taylor inequality(),but my answer is wrong, can someone help me out?

Explanation / Answer

The 5-th derivative is -720/x^7 and then M = 720/0.4^7 ( maximum of the absolute value on [0.4 ; 1.6 ] )

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