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Given: f(x) = 2x2 - 8x + 5 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 2(x+h)2+(x+h)+5 - (2x2-8x+5) h h→0 f ' (x) = lim 2(x2+xh+h2)-8(x+h)+5 - (2x2-8x+5) h h→0 f ' (x) = lim 2x2+xh+2h2-8x-8h+5 + x2+8x-5 h h→0 f ' (x) = lim xh+h2+h h h→0 f ' (x) = lim h(x+h+) h h→0 f ' (x) = lim x+h+ h→0 f ' (x) =   x+