f(x)=x³-5x²+3x+5则,f'(x)=3x²-10x+3f''(x)=6x-10=0 ==> x=5/3当x>5/3时,f''(x)>0,f(x)为凹;当x<5/3时,f''(x)<0,f(x)为凸。拐点为x=5/3
f'(x)=3x² -10x +3 =(3x-1)(x-3) 令f'(x) =0 ,则x1=3,x2=1/3顾拐点为x1=3,x2=1/3两处x<1/3时,f'(x) >0,f(x) 单调增;1/3x>3时,f'(x) >0,f(x) 单调增;