Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$
-$$f ( x ) = 2 x ^ { 2 } + 7 x$$
A) $6 x - 4 h + 14$
B) $4 x ^ { 2 } + 2 h + 7 x$
C) $4 x + 7$
D) $4 x + 2 h + 7$

Question

Quizplus · Accepted Answer

The difference quotient is calculated as $\frac{(2(x+h)^2 + 7(x+h)) - (2x^2 + 7x)}{h}$. Simplifying gives $\frac{(2x^2 + 4xh + 2h^2 + 7x + 7h) - (2x^2 + 7x)}{h} = \frac{4xh + 2h^2 + 7h}{h} = 4x + 2h + 7$.

Compute 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

Compute and Simplify the Difference Quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$