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

Find the differential ($dy$) and evaluate it at $x = 4$ and $dx = 0.2$

So:

$\begin{matrix} dy = f'(4) \times (0.2) \\ dy = 4(4)^3 \times (0.2) \\ dy = 51.2 \\ \end{matrix}$

Am I correct?

2 Answers 2

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Yes. You are indeed correct. You might need to write $dy = 4x^3 dx$ somewhere in the middle since the question also asks "Find the differential $dy$".

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$y=x^4$ $ \frac{dy}{dx}=4x^3$ $ dy=4x^3dx$ at $x=4$ and $dx=0.2$

$ dy=4(4)^3 (0.2)$