Question

Approximate using derivatives. (Must show work using derivatives!) Do not use a calculator:

(1.1)^4 - (1.1)^2

Answer 1

let f(x) = x^4 - x^2
df = (4x^3 - 2x) dx
let x=1, dx=0.1
df ≈ (4-2)(0.1) = 0.2

f(x+dx) ≈ f + df = 0 + 0.2

real value: 0.2541