# How do you use the definition of a derivative to find the derivative of #f(x)= 2x^2 - 3x+4#?

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To find the derivative of ( f(x) = 2x^2 - 3x + 4 ), you use the definition of a derivative, which states that the derivative of a function ( f(x) ) at a point ( x ) is the limit of the difference quotient as the interval around ( x ) shrinks to zero. Applying this definition to ( f(x) ), you calculate the limit of the expression ( \frac{{f(x + h) - f(x)}}{h} ) as ( h ) approaches zero. By evaluating this limit, you obtain the derivative of ( f(x) ) with respect to ( x ). Applying this process to ( f(x) = 2x^2 - 3x + 4 ), you would first compute ( f(x + h) ), then find the difference quotient, and finally evaluate the limit as ( h ) tends to zero. After simplifying the expression and evaluating the limit, you will find the derivative of ( f(x) ), denoted as ( f'(x) ), which represents the rate of change of ( f(x) ) with respect to ( x ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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