Simplify the difference quotient: $$\frac { f ( x + h ) - f ( x ) } { h }$$
-$$x ^ { 4 } - 3 x ^ { 2 } - 1$$
A) $4 x ^ { 3 } h + 6 x ^ { 2 } h ^ { 2 } + 4 x h ^ { 3 } + h ^ { 4 } - 6 x ^ { 2 } h + h ^ { 2 }$
B) $x ^ { 4 } + 4 x ^ { 3 } + 6 x ^ { 2 } h + 4 x h ^ { 2 } + h ^ { 3 } - 6 x ^ { 2 } + h$
C) $4 x ^ { 3 } + 6 x ^ { 2 } h + 4 x h ^ { 2 } + h ^ { 3 } - 6 x - 3 h$
D) $4 x ^ { 3 } + 6 x ^ { 2 } h + 4 x h ^ { 2 } + h ^ { 3 } - 6 x ^ { 2 } + h - 1$

Question

Quizplus · Accepted Answer

The difference quotient simplifies to the derivative of the function as $ h $ approaches zero. The derivative of $ x^4 - 3x^2 - 1 $ is $ 4x^3 - 6x $. The terms involving $ h $ in the difference quotient are $ 6x^2h + 4xh^2 + h^3 - 3h $, which matches option C.

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