stephaniesalas77 stephaniesalas77
  • 02-09-2020
  • Mathematics
contestada

Find the difference quotient and simplify your answer.
f(x) = x2 – 2x + 6,
h = 0
h
f(8 + h) – f(8),

Find the difference quotient and simplify your answer fx x2 2x 6 h 0 h f8 h f8 class=

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LammettHash
LammettHash LammettHash
  • 02-09-2020

We're given that

[tex]f(x)=x^2-2x+6[/tex]

which means

[tex]f(x+h)=(x+h)^2-2(x+h)+6=x^2+2xh+h^2-2x-2h+6[/tex]

When we subtract these, several terms cancel:

[tex](x^2+2xh+h^2-2x-2h+6)-(x^2-2x+6)=2xh+h^2-2h[/tex]

So the difference quotient is

[tex]\dfrac{f(x+h)-f(x)}h=\dfrac{2xh+h^2-2h}h[/tex]

and since h ≠ 0, we can cancel it out to end up with

[tex]\dfrac{f(x+h)-f(x)}h=2x+h-2[/tex]

Now plug in x = 8 (this could have been done at any prior point):

[tex]\dfrac{f(8+h)-f(8)}h=14+h[/tex]

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