Good day sirs i was in class and i didn't understand first order estimate ,could you please explain it to me and show me how to get these exercises done please?

Question1

Example 1 Let f ( ( ) Find the equation of the tangent 1 line to the graph of f at the point (1 , F(1) ) Also, find a first- order estimate for 1 . $ (1.2) 1 - 1 1.2Example 2 Let f(x) = 1" for all x = 0. Ing tall a ) Find the equation of the line tangent to the graph of f at the point ( 16 , $ (16). 4 b ) Find a first- order estimate for 1b. 2bo) A first- order estimate for f near 16 is given by of ~ P' ( 16 ) 01 , where Af = f ( x ) - f( 1b ) and AY = X - 1b