Let y = 4*sqrtx
Estimate the difference delta y when x = 5 using a linear approximation , given that delta x = 0.3

Question

Let y = 4*sqrtx
Estimate the difference delta y when x = 5 using a linear approximation , given that delta x = 0.3

bahrom7893 · Answer

@TuringTest I forgot my linear approximations.

turingtest · Answer

This is phrased strangely for me, but I assume they want you to do is say for $x\approx x_0=5$ we have that$$y(x)\approx y(x_0)+y'(x_0)(x-x_0)\implies y(x)-y(x_0)\approx y'(x_0)(x-x_0)$$$$\Delta y=y(x)-y(x_0),~~~~\Delta x=x-x_0=0.3$$therefor$$\Delta y\approx y'(5)\Delta x$$

turingtest · Answer

@sam0102493 let me know if that makes sense to you