Question

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

• A. $0.32$
• B. $0.032$
• C. $5.68$
• D. $5.968$

Answer 1

Answer: (A)

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 $y=0.32$