Derivatives of Quadratic Polynomials
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Given:f(x) = 3x2 - 6x + 8
Problem:Determine the derivative of f(x) using the definition of a derivative.

f ' (x) = lim
f(x+h) - f(x)
h
h→0

f ' (x) = lim
3(x+h)2+(x+h)+8 - (3x2-6x+8)
h
h→0

f ' (x) = lim
3(x2+xh+h2)-6(x+h)+8 - (3x2-6x+8)
h
h→0

f ' (x) = lim
3x2+xh+3h2-6x-6h+8 + x2+6x-8
h
h→0

f ' (x) = lim
xh+h2+h
h
h→0

f ' (x) = lim
h(x+h+)
h
h→0

f ' (x) = limx+h+
h→0

f ' (x) =  x+