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

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


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

Am I correct?

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up vote 1 down vote accepted

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 $dx=0.2$

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

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