Question #0b1ec

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Answer 1 · 2016-11-03T01:46:38

The difference quotient is #-8#.

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

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

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

Substituting...

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

Distribute

#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#