设函数f(x)=2/3x^3+1/2ax^2+x,a属于R (1)当x=2时,f(x)取得极值,求a的值(2)若f(x)在(0,正无穷)内为增函数,求a的取值范围
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![设函数f(x)=2/3x^3+1/2ax^2+x,a属于R (1)当x=2时,f(x)取得极值,求a的值(2)若f(x)在(0,正无穷)内为增函数,求a的取值范围](/uploads/image/z/1267544-56-4.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3D2%2F3x%5E3%2B1%2F2ax%5E2%2Bx%2Ca%E5%B1%9E%E4%BA%8ER+%EF%BC%881%EF%BC%89%E5%BD%93x%3D2%E6%97%B6%2Cf%28x%29%E5%8F%96%E5%BE%97%E6%9E%81%E5%80%BC%2C%E6%B1%82a%E7%9A%84%E5%80%BC%EF%BC%882%EF%BC%89%E8%8B%A5f%28x%29%E5%9C%A8%EF%BC%880%2C%E6%AD%A3%E6%97%A0%E7%A9%B7%EF%BC%89%E5%86%85%E4%B8%BA%E5%A2%9E%E5%87%BD%E6%95%B0%2C%E6%B1%82a%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
设函数f(x)=2/3x^3+1/2ax^2+x,a属于R (1)当x=2时,f(x)取得极值,求a的值(2)若f(x)在(0,正无穷)内为增函数,求a的取值范围
设函数f(x)=2/3x^3+1/2ax^2+x,a属于R (1)当x=2时,f(x)取得极值,求a的值
(2)若f(x)在(0,正无穷)内为增函数,求a的取值范围
设函数f(x)=2/3x^3+1/2ax^2+x,a属于R (1)当x=2时,f(x)取得极值,求a的值(2)若f(x)在(0,正无穷)内为增函数,求a的取值范围
1.f(x)的导函数为2x^2+ax+1 因为当x=2时,f(x)取得极值,因此2x^2+ax+1当x=2等于0,解得
a=-9/2
2.因为f(x)在(0,正无穷)内为增函数,因此f(x)的导函数2x^2+ax+1 大于等于0时为增函数,那么当2x^2+ax+1最小值4ac-b^2/2a大于等于0时成立,则带入得8-a^2/8大于0,解得a∈【-2更号2,2更号2】
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