Let F(x) = -x^2+2x-3

Question

Three Part Question:

( A )Find the average rate of change of the graph of f(x) between x=c and c+h.

( B )Find the slope of the tangent line of the graph of f(x) at x=c by the definition.

( C )Find f'(-1).

Answer 1

(A).  Average rate of change =

 

 f(c + h) - f(c) =-(c + h)²+2(c + h) - 3 - (-c²+2c-3)

           h                                             h

 

                        = -c²-2ch-h²+2c+2h-3+c²-2c+3

                                                   h

 

                        = -2ch-h²+2h  = h(-2c - h + 2)

                                   h                         h

 

                        = -2c - h + 2

 

(B).  f'(c) = limit as h→0 (-2c - h + 2) = -2c - 0 + 2

                                                              = -2c + 2

 

(C).  f'(-1) = -2(-1) + 2 = 4