The function $f ( x )$ changes value when $x$ changes from $x _ { 0 }$ to $x _ { 0 } + d x$. Find the approximation error $| \Delta f - d f |$. Round your answer, if appropriate.
-$$f ( x ) = x ^ { 3 } , x _ { 0 } = 2 , d x = 0.04$$
A) 0.009664
B) 0.019328
C) 0.014496
D) 0.004832

Question

Quizplus · Accepted Answer

The approximation error is calculated as $| \Delta f - d f |$, where $\Delta f = f(x_0 + dx) - f(x_0)$ and $df = f'(x_0) \cdot dx$. For $f(x) = x^3$, $f'(x) = 3x^2$. Calculate $\Delta f = (2.04)^3 - 2^3$ and $df = 3 \cdot 2^2 \cdot 0.04$. The error is $|\Delta f - df| = |0.249664 - 0.24| = 0.009664$.

The Function f(x)f ( x )f(x) Changes Value When xxx Changes From x0x _ { 0 }x0​

The Function $f ( x )$ Changes Value When $x$ Changes From $x _ { 0 }$