use tangent line approximation (linear approximation) to estimate The cube root of 1234 to 3 decimal places. Hint: the equation should be y=f'(x0)(x-x0)+f(x0)

Question

11^3=1331 can be easily computed using binomial theorem.
I used linear approximation and got 10.733, but it is not correct to 3 decimal places. Cube root of 1234 is 10.726

Answer 1

You are correct. It's just that at x=11, the linear approximation isn't very good when you get var away from 11.

You were not asked to get an approximation which agrees with the true value to 3 places, just to get a value out that far.

Extra credit: how far away from 11 can you go and still have the linear approximation good to three places?