Find the difference quotient and simplify your answer. $$f ( w ) = - 9 w ^ { 2 } + 2 w , \quad \frac { f ( 4 + h ) - f ( 4 ) } { h } , h \neq 0$$
A) $10 + h$
B) $- 70 - 9 w + \frac { 16 } { w }$
C) $2 - 9 w + \frac { 16 } { w }$
D) $2 - 9 h$
E) $- 70 - 9 h$

Question

Quizplus · Accepted Answer

The difference quotient is calculated as $\frac{f(4+h) - f(4)}{h}$. First, find $f(4+h) = -9(4+h)^2 + 2(4+h)$ and $f(4) = -9(4)^2 + 2(4)$. Simplifying both and substituting into the difference quotient gives $-70 - 9h$.

Find the Difference Quotient and Simplify Your Answer f(w)=−9w2+2w,f(4+h)−f(4)h,h≠0f ( w ) = - 9 w ^ { 2 } + 2 w , \quad \frac { f ( 4 + h ) - f ( 4 ) } { h } , h \neq 0f(w)=−9w2+2w,hf(4+h)−f(4)​,h=0

Find the Difference Quotient and Simplify Your Answer $f ( w ) = - 9 w ^ { 2 } + 2 w , \quad \frac { f ( 4 + h ) - f ( 4 ) } { h } , h \neq 0$