已知函数f(x)=mx³+3x²-3x,m属于R,(1)若函数f(x)在x=-1处取得极值,并求f(x)在点M(1,f(1))处的切

问题描述:

已知函数f(x)=mx³+3x²-3x,m属于R,(1)若函数f(x)在x=-1处取得极值,并求f(x)在点M(1,f(1))处的切

f(x)=mx³+3x²-3x
f'(x)=3mx^2+6x-3
f(x)在x=-1处取得极值
f'(1)=0
3m+6-3=0
m=-1
f(x)=x^3+3x^2-3x
f(1)=1
点M(1,1)
f(x)在点M(1,f(1))处的切线方程:y=1