Find $\frac { f ( x + h ) - f ( x ) } { h }$ for the given function.
-$$f ( x ) = x ^ { 3 } - 11$$
A) $3 x ^ { 2 } + 3 x + h ^ { 2 }$
B) $3 x ^ { 2 } + 3 x h + h ^ { 2 } - 22$
C) $3 x ^ { 2 } + 3 x h + h ^ { 2 }$
D) $3 x ^ { 2 } + 3 x + h ^ { 2 } - 22$

Question

Quizplus · Accepted Answer

To find $\frac { f ( x + h ) - f ( x ) } { h }$, first calculate $f(x+h)$: $(x+h)^3 - 11 = x^3 + 3x^2h + 3xh^2 + h^3 - 11$. Then, subtract $f(x) = x^3 - 11$ and divide by $h$: $\frac{(x^3 + 3x^2h + 3xh^2 + h^3 - 11) - (x^3 - 11)}{h} = \frac{3x^2h + 3xh^2 + h^3}{h} = 3x^2 + 3xh + h^2$.

Find f(x+h)−f(x)h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h)−f(x)​

Find $\frac { f ( x + h ) - f ( x ) } { h }$