If y = x⁴ - 10 and if x changes from 2 to 1.99, the change in y is
(a) 0.32 (b) 0.032 (c) 5.68 (d) 5.968

Let x = 2 and x + ∆x = 1.99.

∴ ∆x = 1.99 − 2 = −0.01

$y=x^4-10$ (Given)

Differentiating both sides with respect to x, we get

$\frac{dy}{dx}=4x^3$

$\Rightarrow {\left(\frac{dy}{dx}\right)}_{x=2}=4\times {\left(2\right)}^3=4\times 8=32$

$\therefore ∆y=\left(\frac{dy}{dx}\right)∆x$

$\Rightarrow ∆y=32\times \left(-0.01\right)=-0.32$

Thus, the change in y is 0.32.

Hence, the correct answer is option (a).