If $f ( x ) = x ^ { 2 } - x + 6$, evaluate the difference quotient $\frac { f ( a + h ) - f ( a ) } { h }$.
A) $2 a + h - 6$
B) $2 a - 6$
C) $2 a - h - 6$
D) $h$
E) none of these

Question

Quizplus · Accepted Answer

The difference quotient is $\frac{(a+h)^2 - (a+h) + 6 - (a^2 - a + 6)}{h} = \frac{a^2 + 2ah + h^2 - a - h + 6 - a^2 + a - 6}{h} = \frac{2ah + h^2 - h}{h} = 2a + h - 1$, which is not listed.

If f(x)=x2−x+6f ( x ) = x ^ { 2 } - x + 6f(x)=x2−x+6

If $f ( x ) = x ^ { 2 } - x + 6$