Answer:
a) [tex]f(401) = 3010[/tex], b) [tex]f(400.5) = 3005[/tex], c) [tex]f(399) = 2990[/tex], d) [tex]f(398) = 2980[/tex], e) [tex]f(399.75) = 2997.5[/tex]
Step-by-step explanation:
The estimation of each value can be found by the following value:
[tex]f(x + \Delta x) = f(x) + f'(x)\cdot \Delta x[/tex]
a) [tex]f(401) = 3000 + 10\cdot (401-400)[/tex]
[tex]f(401) = 3010[/tex]
b) [tex]f(400.5) = 3000 + 10\cdot (400.5 - 400)[/tex]
[tex]f(400.5) = 3005[/tex]
c) [tex]f(399) = 3000 + 10\cdot (399 - 400)[/tex]
[tex]f(399) = 2990[/tex]
d) [tex]f(398) = 3000 + 10\cdot (398-400)[/tex]
[tex]f(398) = 2980[/tex]
e) [tex]f(399.75) = 3000 + 10\cdot (399.75-400)[/tex]
[tex]f(399.75) = 2997.5[/tex]
