Calculate the average rate of change for the function [tex]f(x) = -x^4 + 4x^3 - 2x^2 + x + 1[/tex], from [tex]x = 0[/tex] to [tex]x = 1[/tex].
Answer (3)
f ( x ) = − x 4 + 4 x 3 − 2 x 2 + x + 1 f ( 0 ) = − 0 4 + 4 ( 0 ) 3 − 2 ( 0 2 ) + 0 + 1 = 1 f ( 1 ) = − 1 4 + 4 ( 1 3 ) − 2 ( 1 2 ) + 1 + 1 = − 1 + 4 − 2 + 1 + 1 = 3 1 − 0 f ( 1 ) − f ( 0 ) = 1 − 0 3 − 1 = 1 2 = 2
2 ;
The average rate of change of the function f ( x ) = − x 4 + 4 x 3 − 2 x 2 + x + 1 from x = 0 to x = 1 is 2 . This is calculated using the formula 1 − 0 f ( 1 ) − f ( 0 ) , resulting in 2 .
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