Find the difference quotient and simplify your answer. F(x) = x² - x + 1, $\frac { f ( 6 + h ) - f ( 6 ) } { h }$ , h $\neq$ 0 A) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = h + 11$ , h $\neq$ 0 B) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = h + 15$ , h $\neq$ 0 C) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = h + 14$ , h $\neq$ 0 D) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = h + 12$ , h$\neq$ 0 E) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = h + 13$ , h $\neq$ 0

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Quizplus · Accepted Answer

The function given is $F(x) = x^2 - x + 1$. To find the difference quotient $\frac{f(6+h) - f(6)}{h}$, we first calculate $f(6+h)$ and $f(6)$:1. $f(6+h) = (6+h)^2 - (6+h) + 1 = 36 + 12h + h^2 - 6 - h + 1 = h^2 + 11h + 31$2. $f(6) = 6^2 - 6 + 1 = 36 - 6 + 1 = 31$Substituting these into the difference quotient formula gives:$\frac{(h^2 + 11h + 31) - 31}{h} = \frac{h^2 + 11h}{h} = h + 11$, for $h \neq 0$.

Find the Difference Quotient and Simplify Your Answer f(6+h)−f(6)h\frac { f ( 6 + h ) - f ( 6 ) } { h }hf(6+h)−f(6)​

Find the Difference Quotient and Simplify Your Answer $\frac { f ( 6 + h ) - f ( 6 ) } { h }$