Answer to Question #131234 in Calculus for Moel Tariburu

Question

Use an appropriate local linear approximation to estimate the value of (122)^2/3

Answer 1

$f(x)=x^{\frac {2}{3}}$

$f(x_0+\varDelta x)\approx f(x_0)+d[f(x_0)]$

$x_0=125, \varDelta x=-3$

$d[f(x_0)]=f^/(x_0)\times \varDelta x$

$f^/(x)=\frac {2}{3x^{\frac{1}{3}}}$

$d[f(x_0)]=f^/(x_0)\times \varDelta x=\frac {2}{15} \times(-3)=-0.4$

$f(x_0+\varDelta x)\approx f(x_0)+d[f(x_0)] \\ \approx 25-0.4=24.6$