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Home  >>  CBSE XII  >>  Math  >>  Application of Derivatives
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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} $

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1 Answer

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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
answered Aug 9, 2013 by thanvigandhi_1
 

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