Question

If y = x³ + 5 and x changes from 3 to 2.99, then the approximate change is y is _________________.

Answer 1

Let x = 3 and x + ∆x = 2.99.

∴ ∆x = 2.99 − 3 = −0.01

y = x³ + 5 (Given)

Differentiating both sides with respect to x, we get

$\frac{dy}{dx}=3x^2$

$\Rightarrow {\left(\frac{dy}{dx}\right)}_{x=3}=3\times {\left(3\right)}^2=27$

∴ $∆y=\left(\frac{dy}{dx}\right)∆x$

$\Rightarrow ∆y=27\times \left(-0.01\right)=-0.27$

Thus, the approximate change in y is −0.27.


If y = x³ + 5 and x changes from 3 to 2.99, then the approximate change is y is ___−0.27___.