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[f(x+h) - f(x)] / h
[(x+h)^3 - x^3] / h =
[(x^3 + 3x^2*h + 3x*h^2 + h^3) - x^3] / h =
[3x^2*h + 3x*h^2] / h
3x^2 + 3xh
Now, taking the limit of the above expression as h goes to 0, the 3xh goes to 0 and we get an answer of 3x^2.
The derivative is the slope of the tangent line. Evaluating 3x^2 with x = -1, we get a slope of 3.
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