Using Linear Approximation to estimate the max error .

Question

The problem states that a dosage for a dog's is $ D(w) = kw^{2/3} $

where K is a constant and w is equal to 10 kg

I am supposed to find the maximum allowable error "$(\Delta w)$" in w if the percentage of the error $(\Delta D/D) $ must be less than 5%. I started of the question by taking the derivative since

$\Delta f\approx f'(a)\Delta a $

So: $f(10)=k(10)^{2/3} $

and

$f'(10) = 2/3(k(10))^{-1/3}$

Im not sure where to go from here.

Answer 1

Calculate $\Delta D$ from $\Delta D/D(10)=0.05$. Then use this value to approximate $\Delta w \approx dw$ which can be solved from $dD=(2/3)k w^{-1/3} dw$, using $\Delta D \approx dD$.