Posted by **Chris** on Saturday, March 13, 2010 at 12:14am.

Use the fact that (125)^1/3 = 5 and the tangent line approximation to estimate (123)^1/3

- Math -
**Reiny**, Saturday, March 13, 2010 at 7:56am
Let the function be y = x^(1/3)

so we know (125, 5) lies on it, we need (123, ?)

dy/dx = (1/3)x^(-2/3)

at (125,5) , dy/dx = 1/75

the tangent equation is y = (1/75)x + b

but (125,5) is on it

5 = (1/75)(125) + b

5 = 5/3 + b

b = 10/3

tangent line at (125,5) is y = (1/75)x + 10/3

so when x = 123

y = 123/75 + 10/3 = 4.9733

(calculator answer for 123^(1/3) is 4.97319

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