Question

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

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

Answer 1

The correct option is B $0.32$

We have,

$y=x^4-10$
$\Rightarrow \frac{dy}{dx}=4x^3$
Given: $\Delta x=2.00-1.99=0.01$
Now, $\Delta y=4x^3\times \Delta x$
$[\because \Delta y=\frac{dy}{dx}\times \Delta x]$
$\Rightarrow \Delta y=4\times 2^3\times 0.01[\because x=2]$
$\Rightarrow \Delta y=32\times 0.01=0.32$

Therefore, the approximate change in $y$ is $0.32$
Hence, option $a$ is correct.