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.
-$$f ( x ) = x - x ^ { 2 } , x _ { 0 } = 9 , d x = 0.04$$
A) 0.0016
B) 0.272
C) 0.1376
D) 0.136

Question

Quizplus · Accepted Answer

The approximation error is calculated as $| \Delta f - d f |$. First, find $\Delta f = f(x_0 + dx) - f(x_0)$ and $df = f'(x_0) \cdot dx$. For $f(x) = x - x^2$, $f'(x) = 1 - 2x$. Calculate $\Delta f$ and $df$ and find their difference. The error is approximately 0.0016.

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 $x _ { 0 }$