Browse Questions

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

$\begin{array}{1 1} (A)\;.32 \\ (B)\;.032 \\(C)\;5.68\\ (D)\;5.968 \end{array}$

Toolbox:
• For a small change $\Delta \: y$ in the function $y = f(x)$ the change in $x$is $\Delta x$
• $\Rightarrow y+ \Delta y=f(x+ \Delta x)$
Step 1
$y=x^4-10$
$\Delta x = 2.00-1.99$
$= .01$
differentiate w.r.t $x$
$\large\frac{dy}{dx}=4x^3$
$dy=4x^3.dx$
$= 4(2)^3.(0.01)$
$0.32$
Hence the change in $y$ is $dy=0.32$
Hence the correct option is A