Use linear approximation to estimate cube root 794Solutionfx

Use linear approximation to estimate (cube root 7.94)

Solution

f(x+h) = (7.94)^1/3
from linear approximation
xf\'(x) = f(x+h) - f(x).........(1)
here
f(x) = (x)^1/3, where x = 8 & x = -0.06
at x = 8, f(x) = 2
f\'(x) = 1/3 (x)^-2/3
at x = 8
f\'(x) = 1/12
putting the values in (1)
(-0.06)*1/12 = f(x+h) - 2
-0.005 = f(x+h) - 2
f(x+h) = 2-0.005
f(x+h) = 1.995
hence cube root 7.94 = 1.995