Consider the function ( f(x)=x^{2}-x+1 ). Find the average rate of change of ( f(x) ) between the values ( x=3 ) and ( x=5 ).
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f'(3) = (x^2 - x+1) / (x^2 + x+1) f'(3) = 9x^2 - 16x+10 f'(3) = 3x^2 - 10x+30 f'(3) = 30x^2 - 120x+90 f'(3) = 90x^2 - 360x+270 f'(3) = 270x^2 - 1090x+590 f'(3) = 590x^2 - 2940x+1990 The derivative of f(x) at x=3 is therefore 590x^2 - 2940x+1990. Show more…
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