已知函数f(x)=x³-x²-x.(1)求函数f(x)的单调区间; (2)求曲线y=f(x)在点P(-1,f(-1))处的切线方程;
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![已知函数f(x)=x³-x²-x.(1)求函数f(x)的单调区间; (2)求曲线y=f(x)在点P(-1,f(-1))处的切线方程;](/uploads/image/z/6972416-8-6.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dx%26%23179%3B-x%26%23178%3B-x.%281%29%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E5%8D%95%E8%B0%83%E5%8C%BA%E9%97%B4%EF%BC%9B+%282%29%E6%B1%82%E6%9B%B2%E7%BA%BFy%3Df%28x%29%E5%9C%A8%E7%82%B9P%28-1%2Cf%28-1%29%29%E5%A4%84%E7%9A%84%E5%88%87%E7%BA%BF%E6%96%B9%E7%A8%8B%EF%BC%9B)
已知函数f(x)=x³-x²-x.(1)求函数f(x)的单调区间; (2)求曲线y=f(x)在点P(-1,f(-1))处的切线方程;
已知函数f(x)=x³-x²-x.(1)求函数f(x)的单调区间; (2)求曲线y=f(x)在点P(-1,f(-1))处的切线方程;
已知函数f(x)=x³-x²-x.(1)求函数f(x)的单调区间; (2)求曲线y=f(x)在点P(-1,f(-1))处的切线方程;
(1)
f(x)=x³-x²-x.
f'(x)=3x²-2x-1
令f'(x)>0,即3x²-2x-1>0
解得x1
函数递增区间为(-∞,-1/3),(1,+∞)
f(x)递减区间为(-1/3,1)
(2)
f(-1)=(-1)³-(-1)²-(-1)=-1
切点(-1,-1)
切线斜率k=f'(-1)=3+2-1=4
切线方程为
y+1=4(x+1)
即4x-y+3=0