已知函数F(x)=x³+bx²+cx+d的图像过点P(0,2),且在点M(-1,F(-1))处的切线方程为6x-y+7=0(1)求函数Y=F(x)的解析式;(2)求函数Y=F(x)的单调区间.
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![已知函数F(x)=x³+bx²+cx+d的图像过点P(0,2),且在点M(-1,F(-1))处的切线方程为6x-y+7=0(1)求函数Y=F(x)的解析式;(2)求函数Y=F(x)的单调区间.](/uploads/image/z/3150351-63-1.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0F%EF%BC%88x%EF%BC%89%3Dx%26%23179%3B%2Bbx%26%23178%3B%2Bcx%2Bd%E7%9A%84%E5%9B%BE%E5%83%8F%E8%BF%87%E7%82%B9P%EF%BC%880%2C2%EF%BC%89%2C%E4%B8%94%E5%9C%A8%E7%82%B9M%EF%BC%88-1%2CF%EF%BC%88-1%EF%BC%89%EF%BC%89%E5%A4%84%E7%9A%84%E5%88%87%E7%BA%BF%E6%96%B9%E7%A8%8B%E4%B8%BA6x-y%2B7%3D0%EF%BC%881%EF%BC%89%E6%B1%82%E5%87%BD%E6%95%B0Y%3DF%28x%29%E7%9A%84%E8%A7%A3%E6%9E%90%E5%BC%8F%EF%BC%9B%EF%BC%882%EF%BC%89%E6%B1%82%E5%87%BD%E6%95%B0Y%3DF%28x%29%E7%9A%84%E5%8D%95%E8%B0%83%E5%8C%BA%E9%97%B4.)
已知函数F(x)=x³+bx²+cx+d的图像过点P(0,2),且在点M(-1,F(-1))处的切线方程为6x-y+7=0(1)求函数Y=F(x)的解析式;(2)求函数Y=F(x)的单调区间.
已知函数F(x)=x³+bx²+cx+d的图像过点P(0,2),且在点M(-1,F(-1))处的切线方程为6x-y+7=0
(1)求函数Y=F(x)的解析式;
(2)求函数Y=F(x)的单调区间.
已知函数F(x)=x³+bx²+cx+d的图像过点P(0,2),且在点M(-1,F(-1))处的切线方程为6x-y+7=0(1)求函数Y=F(x)的解析式;(2)求函数Y=F(x)的单调区间.
f(0)=d=2,f(x)=x^3+bx^2+cx+2
f'(x)=3x^2+2bx+c
f'(-1)=3-2b+c=6
f(-1)=b-c+1=1
解得b=-3,c=-3
f(x)=x^3-3x^2-3x+2
(2)f'(x)=3x^2-6x-3=3(x^2-2x-1)
解f'(x)>0得x1+√2
增区间(-∞,1-√2)和(1+√2,+∞)
减区间(1-√2,1+√2)