SOLUTION: what is the dy/dx of the tangent of the function of f(x) = x^3 when x = -1 ?

Question 62590: what is the dy/dx of the tangent of the function of f(x) = x^3 when x = -1 ?
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
lim(x -> 0) ( f( x + x1 ) - f(x) )/ x1
lim(x -> 0) ( ( x + x1 )^3 - (x)^3 )/ x1
lim(x -> 0) ( x^3 + 3x^2(x1) + 3x(x1)^2 + (x1)^3 - x^3 )/ x1
lim(x -> 0) ( 3x^2(x1) + 3x(x1)^2 + (x1)^3 )/ x1
lim(x -> 0) (x1)( 3x^2 + 3x(x1) + (x1)^2 )/ x1
lim(x -> 0) 3x^2 + 3x(x1) + (x1)^2
lim(x -> 0) ( f( x + x1 ) - f(x) )/ x1 = 3x^2 + 3x(0) + (0)^2 = 3x^2
f`(x) = 3x^2
f`(-1) = 3(-1)^2 = 3

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