Find and simplify the difference quotient of f $\frac { f ( x + h ) - f ( x ) } { h }$ , h ≠ 0, for the function.
-$$f ( x ) = x ^ { 2 } + 6 x - 8$$
A) 2x+ h - 8
B) $$\frac { 2 x ^ { 2 } + 2 x + 2 x h + h ^ { 2 } + h - 16 } { h }$$
C) 1
D) 2x+ h + 6

Question

Quizplus · Accepted Answer

The difference quotient for the function $f(x) = x^2 + 6x - 8$ is found by substituting $f(x + h)$ and $f(x)$ into the formula $\frac{f(x + h) - f(x)}{h}$. First, find $f(x + h)$:$$f(x + h) = (x + h)^2 + 6(x + h) - 8$$$$= x^2 + 2xh + h^2 + 6x + 6h - 8$$Then, subtract $f(x)$ from $f(x + h)$:$$f(x + h) - f(x) = (x^2 + 2xh + h^2 + 6x + 6h - 8) - (x^2 + 6x - 8)$$$$= 2xh + h^2 + 6h$$Finally, divide by $h$ (and assuming $h \neq 0$):$$\frac{f(x + h) - f(x)}{h} = \frac{2xh + h^2 + 6h}{h}$$$$= 2x + h + 6$$Therefore, the correct answer is 2x + h + 6, which matches choice D.

Find and Simplify the Difference Quotient of F f(x+h)−f(x)h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h)−f(x)​

Find and Simplify the Difference Quotient of F $\frac { f ( x + h ) - f ( x ) } { h }$