TAYLOR POLYNOMIALS AND ERROR IN TAYLOK SERIES Let f(x) = x4 + x3 + x2 + x + 1
(a) Use Taylor's Theorem to compute the remainder R 3 ( x ) in terms of value c that lies between 0 and x.
(b) Give an upper bound on the error assuming x∈ [ − 4 , 4 ].
(c) Compute the exact value of c (in terms of x) so that R 3 ( x ) = f ( x ) − p 3 ( x ) and R 3 ( x ) in part (a) agree.
Note: p 3 ( x ) is the 3rd-order Taylor polynomial.

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step-by-step explanation:

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

i think the answer would be c