SOLUTION: Using differentiation, estimate how much the function f(x)= ax + bln(x) increases by, to 2 decimal places, when a = 85 and b = 19, if x increases from 89 to 89.8

Algebra ->  Functions -> SOLUTION: Using differentiation, estimate how much the function f(x)= ax + bln(x) increases by, to 2 decimal places, when a = 85 and b = 19, if x increases from 89 to 89.8      Log On


   



Question 1021879: Using differentiation, estimate how much the function
f(x)= ax + bln(x)


increases by, to 2 decimal places, when a = 85 and b = 19, if x increases from 89 to 89.8

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Seems like the hard way to do it.
Why not just use f(x)?
.
.
df%2Fdx=a%2Bb%2Fx=85%2B19%2Fx
.
.
I'll take the value of the derivative at the average of the two x values,
x=%2889%2B89.8%29%2F2=89.4
df%2Fdx=85%2B19%2F89.4=85.212
DELTA%2Af=%28df%2Fdx%29%2ADELTA%2Ax
DELTA%2Af=%2885.212%29%2889.8-89%29=68.17
As a comparison,
df=f%2889.8%29-f%2889%29=7650.284-7718.454=68.17002
Pretty good approximation