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`

Options

A. 0.32
B. `-0.32`
C. `5.68`
D. `6.32`

Answer

B

Explanation

let `x=2,x+ Deltax = 1.99.` Then,`Deltax=1.99-2=-0.01.`
Let `dx = Delta x = -0.01`
We have,
`y=x^(4)-10 rArr dy/dx=4x^(3) rArr(dy/dx)_(x=2) =4(2)^(3)=32`
Now, `dy=dy/dx dx`
`rArr " "dy=32(-0.01)=-0.32`
`Deltay=-0.32` approximately" "`[:' Delta" "y cong dy]`
So, approximate change in `y= -0.32.`