Question

已知函数f(x)=x^3+ax^2+bx+c在x=-3/2与x=1时都取的极值,求a,b及f(x)单调区间

Answer 1

f'(x)=3x^2+2ax+b

当x=-3/2和x=1时,f'(x)=0

27/4-3a+b=0

3+2a+b=0

a=3/4,b=-9/2

f'(x)=3x^2+3x/2-9/2=3/2*(2x+3)(x-1)

当x