Question

Use differentials to estimate the value indicated:

1001^(1/3)

Answer 1

So f(1001)~f(1000)+f'(1000)*(?)

Answer 2

function is
\[f(x)=\sqrt[3]{1000+x}\] linearize that one, replace \(x\) by 1

Answer 3

The question mark is where I'm stuck. What do I multiple derivative by?

Answer 4

equation of line tangent to the curve at the point \((1000,10)\) is
\[y-10=m(x-1000)\] and you find \(m\) by taking the derivative and replacing \(x\) by 1000

Answer 5

or better yet, use the function i wrote and the point \((0,10)\)