Question: (a) Use f(x) = lim f ( x + h ) - f(x ) the definition of the derivative of f. Remember, the variable is

(a) Use f(x) = lim f ( x + h ) - f(x ) the definition of the derivative of f. Remember, the variable is h and x is held constant in this limit expression. h -o f'(x ) = lim f ( x + h ) - f (x) h - 0 x th lim - 2(x + h) - [4x3 - 2x] Definition of f. h - o = lim 4X3 + 12x-h + 12xh+ 473 - 2x - 2h - 4X'+ 2x Expand; distribute . h -o = lim 12x h + 12xh2 + 4h3 - 2h Simplify. h -o 12x + 12xh + 4h-_ = lim Factor. h - 0 C = lim Cancel h. X 11 12x - 2 Direct substitution. (b) The figure below shows the graphs f and f' on the same coordinate axes

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