Simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } \text {, if } h \neq 0$ for $f ( x ) = x ^ { 2 } + 4$
A) $\frac { f ( x + h ) - f ( x ) } { h } = x + h$
B) $\frac { f ( x + h ) - f ( x ) } { h } = 2 x$
C) $\frac { f ( x + h ) - f ( x ) } { h } = 2 x + h$
D) $\frac { f ( x + h ) - f ( x ) } { h } = 2 x + h + 8$
E) $\frac { f ( x + h ) - f ( x ) } { h } = 2 x + h ^ { 2 }$

Question

Quizplus · Accepted Answer

The difference quotient simplifies to $\frac{(x + h)^2 + 4 - (x^2 + 4)}{h} = \frac{x^2 + 2xh + h^2 + 4 - x^2 - 4}{h} = \frac{2xh + h^2}{h} = 2x + h$.

Simplify the Difference Quotient f(x+h)−f(x)h, if h≠0\frac { f ( x + h ) - f ( x ) } { h } \text {, if } h \neq 0hf(x+h)−f(x)​, if h=0

Simplify the Difference Quotient $\frac { f ( x + h ) - f ( x ) } { h } \text {, if } h \neq 0$