for a function fx we know f20 52 and f20 03 Estimate a f21

for a function f(x), we know f(-20)= -5.2 and f\'(-20) = 0.3. Estimate a) f(-21) b) f(-23) c) f(-18)

Solution

let f(x) =ax+b

then f\'(x) = a

f\'(-20) =0.3

so a= 0.3

f(x) =0.3x +b

f(-20) =0.3(-20) +b

-5.2 = -6 +b

b = 6 -5.2

b =0.8

f(x) =0.3x +0.8

a)f(-21) = 0.3(-21) +0.8

=-5.5

b).

f(-23) = 0.3(-23) +0.8

= -6.1

c).

f(-18) = 0.3(-18) +0.8

=-4.6