Use Linear Approximation to approximate the cube root of 125.2?

Question

Let f(x)= cube root of x. The linear approximation to f(x) at x=125 can be written in the form of y=mx+b, where m is ? and b is ?

Please help me find "m" and "b"

Answer 1

125 = 5^3

therefor, the cube root for 125  is 5.

f(x) = x ^ (1/3)

from what i can deduct, m can only be obtained depending on x.

and you have:

mx+b = x ^ (1/3)

so b=0    and

     mx = x ^ (1/3)

which means that m = [x ^ (1/3) ] / x = x^[ (1/3) - 1] = x ^ ( -2/3).