find the difference quotient of f; that is, find f(x+h)-f(x)/h, h=0, for the following function. f(x)=x^2-6x+8

h isn't in the denominator (on the right-hand side) in the last line, but I guess it would be better to write 

$$\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}=2x-6$$

.

f(x+h) = (x+h)² - 6(x+h) +8   =  x² + 2hx + h² - 6x - 6h + 8  = x²  - 6x + 8 + h(2x - 6) + h² 

f(x)     =  x² - 6x + 8

 

f(x+h) - f(x) = h(2x - 6) + h² 

 

(f(x+h) - f(x))/h  = 2x - 6 + h

 

When h = 0  (f(x+h) - f(x))/h  → 2x - 6

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Thanks Alan,

Wouldn't you have to say as    $$x\rightarrow 0$$     since h is the denominator and so it cannot equal 0 ?