Question

If f(x) = x⁴ – 10, then find the approximate value of f(2.1).

Answer 1

Since, f(x + h) = f(x) + hf'(x), where h → 0

Here, x = 2, h = 0.1

∴ f(2.1) = f(2) + (0.1)f'(2)   ...(i)

Also, f'(x) = 4x³

f(2) = 4 × 2³

= 32

From (i)

f(2.1) = 16 – 10 + (0.1) × 32

f(2.1) = 6 + 3.2

= 9.2