Question

Find dy and ∆y of y = f(x) = x2 + x at x = 10 when ∆x = 0.1

Answer 1

Given f(x) = x2 + x, x = 10 and ∆x = 0.1

dy = f'(x) ∆x

= (2x + 1) ∆x

= [2(10) + 1] (0.1)

= (21) (0.1) = 2.1

∆y = f(x + ∆x) – f(x)

= (x + ∆x)2 + (x + ∆x) – (x2 + x)

= x2 + 2x ∆x + (∆x)2 + x + ∆x – x2 – x

= 2x ∆x + (∆x)2 + ∆x

= 2(10) (0.1) + (0.1)2 + 0.1

= 2 + 0.01 + 0.1

= 2.11