Question

verify MVT for fext the function. a) f(x) = 2x ^ 3 - 3x ^ 2 - x on [1, 2]​

Answer 1

Answer:

Explanation:

Given:

f(x) = 2x^3-3x^2+1

First note that the sum of the coefficients is 0. That is:

2-3+1 = 0

Hence f(1) = 0 and (x-1) is a factor:

2x^3-3x^2+1 = (x-1)(2x^2-x-1)

Note that the sum of the coefficients of the remaining quadratic is also zero:

2-1-1 = 0

So x=1 is a zero again and (x-1) a factor again:

2x^2-x-1 = (x-1)(2x+1)

From the last linear factor we can see that the remaining zero is x=-1/2

Answer 2

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