Asked by Liz
find the derivative of f(x)=3x^2-x using the limit definition.
Answers
Answered by
Reiny
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)
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)
Answered by
Lizzy
WOW!! You are such a lifesaver!!!!!!!!!=) ...and also very good at math !
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