find the difference quotient of f; that is, find $\frac{f(x + h) - f(x)}{h}$, $h \
eq 0$, for the following function.

$f(x) = x^2 - 8x + 1$

$\frac{f(x + h) - f(x)}{h} =$ (simplify your answer.)

Question

find the difference quotient of f; that is, find $\frac{f(x + h) - f(x)}{h}$, $h \
eq 0$, for the following function.

$f(x) = x^2 - 8x + 1$

$\frac{f(x + h) - f(x)}{h} =$   (simplify your answer.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Function Evaluation", "Difference Quotient" ], "new_concepts": [], "current_concepts": [ "Function Evaluation", "Difference Quotient", "Polynomial Evaluation" ] } ## Evaluate the function at x + h Using the *Function Evaluation* knowledge point $$ \begin{aligned} f(x+h) &= (x+h)^2 - 8(x+h) + 1 \ &= x^2 + 2xh + h^2 - 8x - 8h + 1 \end{aligned} $$ ## Set up the difference quotient numerator Using the *Difference Quotient* knowledge point $$ \begin{aligned} f(x+h) - f(x) &= (x^2 + 2xh + h^2 - 8x - 8h + 1) - (x^2 - 8x + 1) \ &= 2xh + h^2 - 8h \end{aligned} $$ ## Divide by h and simplify Using the *Difference Quotient* knowledge point $$ \begin{aligned} \frac{f(x+h) - f(x)}{h} &= \frac{2xh + h^2 - 8h}{h} \ &= \frac{h(2x + h - 8)}{h} \ &= 2x + h - 8 \end{aligned} $$ Find the difference quotient of f; that is, find $\frac{f(x+h)-f(x)}{h}$, $h eq 0$, for the following function. $f(x) = x^2 - 8x + 1$ $\frac{f(x+h)-f(x)}{h} =$ $2x + h - 8$ (Simplify your answer.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Difference Quotient" ] }

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QUESTION IMAGE

Question

Explanation:

Evaluate the function at x + h

Set up the difference quotient numerator

Divide by h and simplify

Answer: