Practicing Success
If $y=x^4-10$ and if x changes from 2 to 1.99, than the approximate change in y is |
0.32 -0.32 5.68 6.32 |
-0.32 |
Let $x=2, x+\Delta x=1.99$. Then, $\Delta x=1.99-2=-0.01$ Let $d x=\Delta x=-0.01$ We have, $y=x^4-10 \Rightarrow \frac{d y}{d x}=4 x^3 \Rightarrow\left(\frac{d y}{d x}\right)_{x=2}=4(2)^3=32$ Now, $d y=\frac{d y}{d x} d x$ $\Rightarrow d y=32(-0.01)=-0.32$ $\Rightarrow \Delta y=-0.32$ approximately [∵ Δy ≅ dy] So, approximate change in $y=-0.32$ |