Find $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$ . $f ( x ) = x ^ { 2 } - 7 x$
A) $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = 2 x - 9$
B) $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = 2 x - 7$
C) $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = 2 x + 7$
D) $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = - ( 2 x - 7 )$
E) $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = 2 x + 6$

Question

Find $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$ .  $f ( x ) = x ^ { 2 } - 7 x$  
A) $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = 2 x - 9$
B) $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = 2 x - 7$
C) $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = 2 x + 7$
D) $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = - ( 2 x - 7 )$
E) $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = 2 x + 6$

Quizplus · Accepted Answer

This limit represents the derivative of $f(x) = x^2 - 7x$ with respect to $x$. Differentiating $f(x)$ gives $f'(x) = 2x - 7$, which matches choice B.

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Find $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$