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Given the function $$f(x) = x^4$$

If you approximated $(4.2)^4$ by computing $4^4$, what approximate error does the differential indicate there would be between your approximate answer and the exact value?

What am I supposed to do in this problem?

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Use$$ \Delta f = f\left(x+\Delta x\right) - f\left(x\right) \approx f'\left(x\right) \Delta x. $$

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    Ok so I have if I plug in $4$, $dy = 51.2$. So do I just plug in $4.2$ too?2012-10-31
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    No, $f'\left(x\right) \Delta x$ is the first order error in $\Delta x$ from approximating $f\left(x+\Delta x\right)$ by $f\left(x\right)$. 51.2 is the (first order) error in approximating $4.2^4$ by $4^4$.2012-10-31
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    Ok, so what do I do next?2012-10-31
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    Gerry was right. Next, you think more about what you have calculated.2012-10-31