已知函数f(x)=(1/3)x的3次方-x的2次方+ax+b的图像在点p(0,f(0))处的切线是3x-y-2=0.求a,b的值.2设t属于(-2,-1),函数g(x)=f(x)+(m-3)x在(t,正无穷)上为增函数,求m的取值范围
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/21 06:06:17
![已知函数f(x)=(1/3)x的3次方-x的2次方+ax+b的图像在点p(0,f(0))处的切线是3x-y-2=0.求a,b的值.2设t属于(-2,-1),函数g(x)=f(x)+(m-3)x在(t,正无穷)上为增函数,求m的取值范围](/uploads/image/z/6894595-19-5.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3D%281%2F3%29x%E7%9A%843%E6%AC%A1%E6%96%B9-x%E7%9A%842%E6%AC%A1%E6%96%B9%2Bax%2Bb%E7%9A%84%E5%9B%BE%E5%83%8F%E5%9C%A8%E7%82%B9p%280%2Cf%280%29%29%E5%A4%84%E7%9A%84%E5%88%87%E7%BA%BF%E6%98%AF3x-y-2%3D0.%E6%B1%82a%2Cb%E7%9A%84%E5%80%BC.2%E8%AE%BEt%E5%B1%9E%E4%BA%8E%28-2%2C-1%29%2C%E5%87%BD%E6%95%B0g%28x%29%3Df%28x%29%2B%28m-3%29x%E5%9C%A8%28t%2C%E6%AD%A3%E6%97%A0%E7%A9%B7%29%E4%B8%8A%E4%B8%BA%E5%A2%9E%E5%87%BD%E6%95%B0%2C%E6%B1%82m%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
已知函数f(x)=(1/3)x的3次方-x的2次方+ax+b的图像在点p(0,f(0))处的切线是3x-y-2=0.求a,b的值.2设t属于(-2,-1),函数g(x)=f(x)+(m-3)x在(t,正无穷)上为增函数,求m的取值范围
已知函数f(x)=(1/3)x的3次方-x的2次方+ax+b的图像在点p(0,f(0))处的切线是3x-y-2=0.求a,b的值.2设t属于(-2,-1),函数g(x)=f(x)+(m-3)x在(t,正无穷)上为增函数,求m的取值范围
已知函数f(x)=(1/3)x的3次方-x的2次方+ax+b的图像在点p(0,f(0))处的切线是3x-y-2=0.求a,b的值.2设t属于(-2,-1),函数g(x)=f(x)+(m-3)x在(t,正无穷)上为增函数,求m的取值范围
1.f'(x)=x^2-2x+a为各点切线的斜率
则f'(0)=a=3
切线方程x=0时,y=-2,即(0,-2)在f(x)上,f(0)=-2,得b=-2
2.x>t时,g'(x)=f'(x)+(m-3)=x^2-2x+m=(x-1)^2+m-1>=0恒成立
而-2
x=0,f(0)=3x-2=-2=b,f(x)求导=x^2-2x+a,又令x=0则a=3 .................g(x)求导=x^2-2x+m=(x-1)^2+m-1 在(t,正无穷)上恒为正 则m-1恒大于等于0
1.f(0)=b,切点(0,b)在3x-y-2=0上,代入得b=-2,切线斜率3,f'(x)=x^2-2x+a,f'(1)=a-1=3,a=4.
2.当x>-2时g'(x)=f'(x)+m-3=x^2-2x+m+a-3=x^2-2x+m+1>=0,g'(x)=x^2-2x+m+1对称轴为x=1,
必有△=4-4(m+1)<=0,m>=0
f(0)=b,P(0,f(0))在3x-y-2=0上,f(0)=2,b=2.
f'(x)=x^2-2x+a,f'(0)=a,它等于3x-y-2=0的斜率,故a=3
a=3,b=2.
g(x)=(1/3)x^3-x^2+mx+2,
g'(x)=x^2-2x+m在(t,正无穷)上大于0,y=x^2-2x在x=1达最小值-1
故m>=1