If `y=x^4-10` and if `x` changes from 2 to 1.99, what is the approximate change in `y` ? Also, find the changed value of `ydot`

Explanation

Given ,
`y=x^4-10`
`Δx=2.00−1.99=0.01`

differentiating w.r.t .`x`.
`(dy)/(dx)=4x^3`
`=>dy=4x^3dx`
`=4(2)^3(0.01)`
`=0.32`(approx)
so, the approximate change in `y=0.32`
when `x=2`
`y=2^4-10=6`
so,changed value of `y=y+Deltay`
`=6+0.32`
`=6.32`