Question

Suppose that f (400 )equals3000 and f prime (400 )equals10. Estimate each of the following. ​(a) f (401 )​(b) f (400.5 )​(c) f (399 )​(d) f (398 )​(e) f (399.75 )

Answer 1

a)
`f(401) = 3010`, b)
`f(400.5) = 3005`, c)
`f(399) = 2990`, d)
`f(398) = 2980`, e)
`f(399.75) = 2997.5`

Explanation:

The estimation of each value can be found by the following value:

`f(x + \Delta x) = f(x) + f'(x)\cdot \Delta x`

a)
`f(401) = 3000 + 10\cdot (401-400)`

`f(401) = 3010`

b)
`f(400.5) = 3000 + 10\cdot (400.5 - 400)`

`f(400.5) = 3005`

c)
`f(399) = 3000 + 10\cdot (399 - 400)`

`f(399) = 2990`

d)
`f(398) = 3000 + 10\cdot (398-400)`

`f(398) = 2980`

e)
`f(399.75) = 3000 + 10\cdot (399.75-400)`

`f(399.75) = 2997.5`