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How do you find the derivative of $f(x) = 7x^2 - 3$ using the limit definition?

1 Answer

Jun 22, 2016

$14x$

Explanation:

f $'(x) = lim_{h \to 0} ( (7(x+h)^2 - 3) - (7x^2 - 3))/h$

$= lim_{h \to 0} ( (7(x^2+2xh + h^2) - 3) - (7x^2 - 3))/h$

$= lim_{h \to 0} ( 7x^2+14xh + 7h^2 - 3 - 7x^2 + 3)/h$

$= lim_{h \to 0} ( 14xh + 7h^2 )/h$

$= lim_{h \to 0} 14x + 7h = 14x$

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