# Using the limit definition, how do you find the derivative of #f(x) = 3x^2 + 8x + 4 #?

Applying the limit definition, we obtain

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To find the derivative of ( f(x) = 3x^2 + 8x + 4 ) using the limit definition, follow these steps:

- Begin with the definition of the derivative: ( f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} ).
- Substitute the given function ( f(x) = 3x^2 + 8x + 4 ) into the formula.
- Expand the function ( f(x + h) ) and ( f(x) ).
- Simplify the expression by combining like terms.
- Take the limit as ( h ) approaches 0.
- Calculate the derivative.

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