Simplify the difference quotient: $$\frac { f ( x + h ) - f ( x ) } { h }$$
-$$6 x ^ { 3 } + 6$$
A) $18 h x ^ { 2 } + 18 x h ^ { 2 } + 6 h ^ { 3 }$
B) $x ^ { 3 } + 18 x ^ { 2 } + 18 x h + 6 h ^ { 2 }$
C) $18 x ^ { 2 } + 18 x h + 6 h ^ { 2 } + 6$
D) $18 x ^ { 2 } + 18 x h + 6 h ^ { 2 }$

Question

Quizplus · Accepted Answer

To simplify the given difference quotient with $f(x) = 6x^3 + 6$, we substitute $f(x+h)$ and $f(x)$ into the formula. Simplifying the expression leads to the elimination of the constant term and results in $18x^2 + 18xh + 6h^2$, which matches option D.

Simplify the Difference Quotient f(x+h)−f(x)h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h)−f(x)​

Simplify the Difference Quotient $\frac { f ( x + h ) - f ( x ) } { h }$