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Given: f(x) = 3x2 + 10x - 4 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)-4 - (3x2+10x-4) h h→0 f ' (x) = lim 3(x2+xh+h2)+10(x+h)-4 - (3x2+10x-4) h h→0 f ' (x) = lim 3x2+xh+3h2+10x+10h-4 + x2-10x+4 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+