Difference quotient for $$$f{\left(x \right)} = x^{2} + 6 x - 7$$$
Your Input
Find the difference quotient for $$$f{\left(x \right)} = x^{2} + 6 x - 7$$$.
Solution
The difference quotient is given by $$$\frac{f{\left(x + h \right)} - f{\left(x \right)}}{h}$$$.
To find $$$f{\left(x + h \right)}$$$, plug $$$x + h$$$ instead of $$$x$$$: $$$f{\left(x + h \right)} = \left(x + h\right)^{2} + 6 \left(x + h\right) - 7$$$.
Finally, $$$\frac{f{\left(x + h \right)} - f{\left(x \right)}}{h} = \frac{\left(\left(x + h\right)^{2} + 6 \left(x + h\right) - 7\right) - \left(x^{2} + 6 x - 7\right)}{h} = h + 2 x + 6$$$.
Answer
The difference quotient for $$$f{\left(x \right)} = x^{2} + 6 x - 7$$$A is $$$h + 2 x + 6$$$A.