Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.
-$$f ( x ) = x ^ { 2 } + 3 x + 7$$
A) $2 x + h + 3$
B) 1
C) $2 x + h + 7$
D) $\frac { 2 x ^ { 2 } + 2 x + 2 x h + h ^ { 2 } + h + 14 } { h }$

Question

Quizplus · Accepted Answer

To find the difference quotient, substitute $f(x) = x^2 + 3x + 7$ into the formula. This gives $\frac{(x+h)^2 + 3(x+h) + 7 - (x^2 + 3x + 7)}{h}$. Simplifying inside the numerator gives $x^2 + 2xh + h^2 + 3x + 3h + 7 - x^2 - 3x - 7$, which simplifies further to $2xh + h^2 + 3h$. Dividing each term by $h$ results in $2x + h + 3$.

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