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Fx=3x^2+4x+4/x^2+x+1求极值点,和极值

f(x)=(3x²+4x+4)/(x²+x+1) = (3x²+3x+3+x+1)/(x²+x+1) = 3 + (x+1)/(x²+x+1) = 3 + (x+1)/{(x+1)²-(x+1)+1} 当x=-1时: f(-1)=3+0=3 当x≠-1时: f(x) = 3 + 1/{(x+1) - 1 + 1/(x+1)} = 3 + 1/g(x) 其中g(x) = (x+...

见图

f'(x) =3x² - 6x + 1 令f'(x) = 0, 求得极值点 x = (3± √6)/3 f(x) 在 (-∞,(3- √6)/3)增函数 ((3-√6)/3,(3+√6)/3)减函数 ((3+√6)/3,+∞)增函数 所以x = (3-√6)/3取极大值,代入f(x) 计算~~~~ 所以x = (3+√6)/3取极小...

f(x) = 1/3x³-4x+4 f ′(x) = x²-4 = (x+2)(x-2) ∵x属于【0,a】 ∴x+2>0 a≤2时,单调减: 最大值f(0)=0-0+4 = 4 最小值f(a) = 1/3a³-4a+4 a>2时,0<x<2单调减,2<x<a单调增 极小值f(2) = 1/3*2³-4*2+4 = 4/3 极小值就...

f'(x)=3x^2+2x-a=0在(-1,1)内只有一个根 故f'(-1)f'(1)

题干不全,无法作答

f(x) = ax³+x² f ′(x) = 3ax²+2x 在x=-4/3处取得极值 f ′(-4/3) = 3a*16/9-8/3 = 0 a=1/2 f(x) = 1/2x³+x² g(x) = e^x*f(x) = e^x*(1/2x³+x²) g ′(x) = e^x*(1/2x³+x²) + e^x*(3/2x²+2x) = e...

y'=6x²-6x-12=6(x²-x-2)=6(x-2)(x+1), 得极值点x=2, -1 y"=6(2x-1), 得拐点x=1/2 单调增区间:x>2, 或x

f(x)=(3x²+ax)/e^xf'(x)=(6x+a)/e^x-(3x²+ax)/e^x=06x+a=3x²+ax3x^2-(a-6)x-a=0f(0)=0f'(0)=-a则a=0f(x)=3x²/e^xf(1)=3/ef'(x)=(6x-3x^2)/e^xf'(1)=3/e设切线方程为y=3/e*x+b则3/e+b=3/e,b=0y=3x/e

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