Find and simplify the difference quotient $$\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$$ for the given function.
-$$f ( x ) = x ^ { 2 } + 8 x - 9$$
A) $2 x + h - 9$
B) $2 x + h + 8$
C) 1
D) $\frac { 2 x ^ { 2 } + 2 x + 2 x h + h ^ { 2 } + h - 18 } { h }$

Question

Quizplus · Accepted Answer

To find the difference quotient for $f(x) = x^2 + 8x - 9$, we substitute $f(x + h)$ and $f(x)$ into the formula. First, calculate $f(x + h) = (x + h)^2 + 8(x + h) - 9$. Expanding this gives $x^2 + 2xh + h^2 + 8x + 8h - 9$.Subtract $f(x) = x^2 + 8x - 9$ from $f(x + h)$ to get $2xh + h^2 + 8h$.Divide the result by $h$ (and assuming $h \neq 0$) to simplify to $2x + h + 8$.

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 $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$