Let f(x) = x ^3. The equation of the tangent line to f(x) at x = 5 is y=75x - 250
What is the approximation for 4.6 ^3?
just plug in x:
y = 75(4.6)-250
That gives you an approximation of 95, versus the real value of 97.336
Not too good, but then 4.6 is not terrifically close to 5, either.