Problem : Calculate the derivative of f (x) = x 2 at x = 1 .Substituting 1 for x 0 in the formula for the derivative, we have
|=||2 + Δx|
Problem : Find the vertex of the parabola f (x) = x 2 + 2x + 2 using the derivative.At the vertex, the tangent line to the graph will be horizontal, with slope 0 . Therefore, we search for an x such that f'(x) = 0 . We have
|=||limΔx→02x + 2 + Δx|
|=||2(x + 1)|
Problem : Find the equation of the tangent line to the graph of f (x) = x 3 at x = 2 .First we compute f'(2) :
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