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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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