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

0.32

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0.032

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5.68

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5.968

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Solution

The correct option is A $0.32$
$y = x^{4} - 10$
$Δ x = 2.00 - 1.99 = 0.01$
differentiating w.r.t .x.
$\frac{d y}{d x} = 4 x^{3}$
$d y = 4 x^{3} d x$
$= 4 (2)^{3} . (0.01)$
$= 0.32$

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