Question

calculus help
http://prntscr.com/cy14hx

Answer 1

\(\color{black}{\displaystyle f(x)= f(a)+f'(a)(x-a)}\)

Answer 2

(This is at x=2, or near x=2.)

\(\color{black}{\displaystyle f(x)= f(2)+f'(2)(x-2)}\)
\(\color{black}{\displaystyle f(x)= 5-3(x-2)}\)
\(\color{black}{\displaystyle f(k)= 5-3(k-2)}\)

you want \(\color{black}{\displaystyle f(k)=k}\), so we call \(\color{black}{\displaystyle f(k) }\), \(\color{black}{\displaystyle k}\).

\(\color{black}{\displaystyle k= 5-3(k-2)}\).

Answer 3

Yes. Compare this to the familiar y=mx+b, where m is the slope of the straight line and f(a) is the initial value (which in some cases would be the y-intercept, (0,b).

Answer 4

i just solve for k then?