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 for the function $f(w) = -9w^2 + 2w$ is calculated by substituting $w = 4 + h$ and $w = 4$ into the function, then finding the difference and dividing by $h$. Simplifying the expression $\frac{-9(4+h)^2 + 2(4+h) + 9(4)^2 - 2(4)}{h}$ results in $-70 - 9h$.

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 $f ( w ) = - 9 w ^ { 2 } + 2 w , \quad \frac { f ( 4 + h ) - f ( 4 ) } { h } , h \neq 0$