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?
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?
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 $dy$".
$y=x^4$ $ \frac{dy}{dx}=4x^3$ $ dy=4x^3dx$ at $x=4$ and $dx=0.2$
$ dy=4(4)^3 (0.2)$