Question

Use linear approximation, i.e. the tangent line, to approximate cubed root { 1.1 }. The equation of the tangent line to f(x) at x = 1 can be written in the form y = mx+b.
Show your work. Do not use a calculator.

Answer 1

y = x^(1/3)

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

at x = 1, y = 1 and dy/dx = (1/3)=m

y = 1 + (1/3) (x-1)

y = (1/3) x + 2/3

at x = 1.1
y = (1/3)(1.1) + 2/3
y = (1/3) 3.1