Question #0b1ec

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Answer 1 · 2016-11-03T01:46:38

The difference quotient is $- 8$ $-8$ .

$\frac{f (x + h) - f (x)}{h}$ $frac{color(red)(f(x+h))-color(blue)(f(x))}{h}$ for $f (x) = - 8 x + 1$ $color(blue)(f(x)=-8x+1)$

Replace $x$ $x$ with $x + h$ $x+h$ to find $f (x + h)$ $f(x+h)$

$f (x + h) = - 8 (x + h) + 1$ $color(red)(f(x+h)=-8(x+h)+1)$

Substituting...

$\frac{- 8 (x + h) + 1 - (- 8 x + 1)}{h}$ $frac{color(red)(-8(x+h)+1)-color(blue)((-8x+1))}{h}$

Distribute

$\frac{- 8 x - 8 h + 1 + 8 x - 1}{h}$ $frac{-8x-8h+1+8x-1}{h}$

Combine like terms.

$frac{cancel(-8x)-8h+cancel(1)+cancel(8x)-cancel1}{h}$

$(-8h)/h$

$(-8cancelh)/cancelh$

$-8$