Find and simplify the difference quotient $$\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$$ for the given function.
-$$f ( x ) = 3 x ^ { 2 }$$
A) $\frac { 3 \left( 2 x ^ { 2 } + 2 x h + h ^ { 2 } \right) } { h }$
B) $3 ( 2 x + h )$
C) 3
D) $\frac { 6 } { h } + x + 3 h$

Question

Quizplus · Accepted Answer

To find the difference quotient for $f(x) = 3x^2$, substitute $f(x+h)$ and $f(x)$ into the difference quotient formula. $f(x+h) = 3(x+h)^2 = 3(x^2 + 2xh + h^2)$. Then, $f(x+h) - f(x) = 3(x^2 + 2xh + h^2) - 3x^2 = 3(2xh + h^2)$. Simplifying the difference quotient gives $\frac{3(2xh + h^2)}{h} = 3(2x + h)$.

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

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