(1)∵点P(3,3)在曲线C上,∴a?33-32+3=3,解得a= 1 3 ;(2)∵f′(x)=x2-2x+1,∴在点P(3,3)处的切线斜率k=32-2×3+1=4,曲线C在点P(3,3)处的切线方程为:y-3=4(x-3),即4x-y-9=0.