Linear approximation practice question 5

Which number near 3.002 makes $x^{4}$ easy to work out exactly? Linearise $x^{4}$ there and step along the tangent line.

Take $f(x) = x^{4}$ and base point $a = 3$, where $f(3) = 81$ and $f'(3) = 4\cdot 27 = 108$.

$f(3.002) \approx f(3) + f'(3)\,(3.002 - 3)$. The step is $0.002$.