If y=x4−10 and if x changes from 2 to 1.99, than the approximate change in y is

# If $y={x}^{4}-10$ and if $x$ changes from 2 to 1.99, than the approximate change in $y$ is

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### Solution:

Let $x=2,x+\mathrm{\Delta }x=1.99.$ Then, $\mathrm{\Delta }x=1.99-2=-0.01.$

Let $dx=\mathrm{\Delta }x=-0.01$

We have,

$y={x}^{4}-10⇒\frac{dy}{dx}=4{x}^{3}⇒{\left(\frac{dy}{dx}\right)}_{x=2}=4\left(2{\right)}^{3}=32$

Now, $dy=\frac{dy}{dx}dx$

approximately $\left[\because \mathrm{\Delta }y\cong dy\right]$

So, approximate change in $y=-0.32.$

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