Question

If $y=2x^3-2x^2+3x-5$, then for $x=2$ and $\mathrm{\Delta }x=0.1$ value of $\mathrm{\Delta }y$ is:

• (A) 2.002
• (B) 1.9
• (C) 0
• (D) 0.9

Answer 1

The Correct Option is B

Explanation:
Given:$y=2x^3-2x^2+3x-5$$\Rightarrow \frac{dy}{dx}=6x^2-4x+3$$\Rightarrow {\left(\frac{dy}{dx}\right)}_{x=2}=24-8+3=19$$\because \mathrm{\Delta }y={\left(\frac{dy}{dx}\right)}_{x=2}\mathrm{\Delta }x$$\Rightarrow \mathrm{\Delta }y=19\times (0.1)=1.9$Hence, the correct option is (B).