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

Answer:

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

Step-by-step 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) $f(399.75) = 3000 + 10\cdot (399.75-400)$

$f(399.75) = 2997.5$