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  4. If y = x4 - 10 and if x changes from 2 to 1.99, what is the change in y

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Q. If $y = x^4 - 10$ and if $x$ changes from $2$ to $1.99$, what is the change in $y$

Application of Derivatives

Solution:

Let $x=2$, $x + \Delta x= 1.99$.
Then, $\Delta x= 1.99-2 =-0.01$
Let $dx = \Delta x = - 0.01$
We have, $y = x^4 - 10$
$\Rightarrow \frac{dy}{dx}=4x^{3}$
$\Rightarrow \left(\frac{dy}{dx}\right)_{x = 2} = 4\left(2\right)^{3} = 32$
$\therefore dy=\frac{dy}{dx}dx$
$dy = 32 \left(-0.01\right) = -0.32$
$\Rightarrow \Delta y = -0.32$ approximately $\left[\because \:\Delta y \cong dy\right]$
So, change in $y = 0.32$