dy

ประมาณค่า $$ \sqrt[4]{624} +\sqrt{624} \\ $$
วิธีทำ

\begin{align} \cssId{Step1}{ ให้ f(x)= \sqrt[4]{x} +\sqrt{x} } \\ \cssId{Step2}{ ดังนั้น f(624) = f(625+(-1) ) \approx f(625)+f'(625)(-1) } \\ \cssId{Step3}{ f(625)=\sqrt[4]{625}+\sqrt{625} = 5+25 = 30 } \\ \cssId{Step4}{ f'(x) = \frac{1}{4}x^{-3/4} + \frac{1}{2} x^{-1/2} } \\ \cssId{Step5}{ f'(625) = \frac{1}{4}(625)^{-3/4} + \frac{1}{2} (625)^{-1/2} =\frac{1}{500} +\frac{1}{50} =0.022 } \\ \cssId{Step6}{ ดังนั้น \sqrt[4]{624} +\sqrt{624} \approx 30+0.022*(-1) = 30-0.022 =29.978 } \\ \end{align}