Consider the function f ( x ) = x 2 + 2…
Consider the function f ( x ) = x 2 + 2 x + 1 . The slopes of secant lines from the indicated ( b , f ( b ) ) point to the point ( 0 , 1 ) on the graph of f ( x ) are given in the tables below. x = b – 0 . 5 – 0 . 1 – 0 . 01 – 0 . 001 secant slope 1 . 5 1 . 9 1 . 99 1 . 999 x = b 0 . 5 0 . 1 0 . 01 0 . 001 secant slope 2 . 5 2 . 1 2 . 01 2 . 001 (a) Use this information to estimate f ‘ ( 0 ) . f ‘ ( 0 ) = (b) Write the equation of the line tangent to the graph of f ( x ) at ( 0 , 1 ) . y =