Question

I'm having trouble estimating derivatives...
suppose that f(x) is a function with f(100)=35 and f '(100)=3. estimate f(102)

Answer 1

that was wrong, sorry. you are supposed to find the line through the point
\[(100,35)\] with slope 3
use the point slope formula

Answer 2

line is
\[y-35=3(x-100)\] or
\[y=3(x-100)+35\] now replace x by 102 to get
\[y=3(2)+35\] or
\[y=41\] and that is your "estimate"

Answer 3

notice that you could have done this more or less in your head reasoning that the slope is 3, so if you go to the right 2 you go up 6 and so if you start at 35 you end up at 41