If y = x⁴ – 10 and if x changes from 2 to 1.99, what is the change in y

Given y = x⁴ – 10

Differentiating on both sides with respect to x, we get

Applying the power rule we get

It is also given that the value of x changes from from 2 to 1.99, so the change in x is

Δx=2-1.99=0.01

So the change in y becomes,

Substituting the corresponding values we get

⇒ Δy=4x³×(0.01)

Now at x=2, the change in y becomes

⇒ Δy_x=2=4(2)³×(0.01)

⇒ Δy_x=2=4× 8×(0.01)

⇒ Δy_x=2=0.32

Hence the change in y is 0.32.