Question

函数f(x)=1/4x^4+1/3ax^3-a^2x^2在区间[-1,1]上的最大值

Answer 1

令f′(x)=x^3+ax^2-2a^2x=x(x+2a)(x-a)=0,

则x1=0,x2=-2a,x3=a.

∵f(0)=0,

f(-2a)=-8/3a^4≤0,

f(a)=-13/12a^4≤0,

f(-1)=-13/12