Answer to Question #7359 in Calculus for molly

Question

if C(50)=4600 and Cprime(50)=28 estimate C(55)

Answer 1

Use the formula:
C(x+t) ~ C(x) + t C'(x)

We have that
x =
50
t = 5
C(x) = 4600
C'(x) = 28,
whence
C(55) = C(50+5) =
C(x+t) =
= C(50) + 5 * C'(50) =
= 4600 + 5 * 28
=
= 4600 + 140 =
= 4740