find the derivative of f(x)=3x^2-x using the limit definition.

Answer 1

f(x) = 3x^2 - x
f(x+h) = 3(x+h)^2 - (x+h)
= 3x^2 + 6xh + 3h^2 - x - h

dy/dx = lim [ ( f(x+h) - f(x)]/h , as h ----> 0
= lim (3x^2 + 6xh + 3h^2 - x - h - 3x^2 + x)/h
= lim (6xh + 3h^2 - h)/h
= lim 6x + 3h - 1 , as h --->0
= 6x - 1

(the h--> 0 should be under the word "lim" in each line)

Answer 2

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