(a) From this definition we have the following. f( 4 + h ) - f(4 ) f'(4) = lim h - 0 h 6 ( 4 + 1 ) + 4 - 1( 4 ) 2 - 6 ( 4 ) + 41 = lim h - 0 h 16 + 24 - 6h + 4+4 = lim h - 0 h = lim h - 0 h = lim h - 0 (b) f'(a) = lim f(ath ) - f(a ) h - 0 h = lim 6 ( a + h ) + 4 - [a2 - 62 + 4] h - 0 h = lim - 62 - 6h + 4 - a2 + 6a - 4 h - 0 h = lim h - 0 h = lim As a check on our work in part (a), notice that if we let a = 4, then f'(a) = f'(4) = Need Help? Read It