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  4. If y = 2x3 - 2x2 + 3x - 5, then for x = 2 and Δ x = 0.1 value of Δ y is

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Q. If $y = 2x^3 - 2x^2 + 3x - 5$, then for $x = 2$ and $Δ \,x = 0.1$ value of $Δ \, y$ is

WBJEEWBJEE 2011Application of Derivatives

Solution:

Given, $y=2 x^{3}-2 x^{2}+3 x-5$
$\Rightarrow \frac{d y}{d x}=6 x^{2}-4 x+3$
$\Rightarrow \left(\frac{d y}{d x}\right)_{x=2}=24-8+3=19$
$\because \Delta y=\left(\frac{d y}{d x}\right)_{x=2} \Delta x$
$\Rightarrow \Delta y=19 \times(0.1)$
$=1.9$