Question

Use linear approximation (or differentials) to estimate the given number: 3 square root 1001

Answer 1

\[\sqrt[3]{1001}\]

Answer 2

for function f(x) the linear approximation at point "a" is:
\[f(x) \approx f'(a)(x-a) + f(a)\]
for this problem
f(x) = x^1/3
let a = 1000