英文版specify the inflection point P(拐点) of the curve f(x)=-x立方

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英文版
specify the inflection point P(拐点) of the curve f(x)=-x立方+3x方-7 also find thr equation of the tangent line t at P
第2问让求P点的切线,而P点是拐点,怎么会有切线?

f(x)=-x³+3x²-7
f'(x)=-3x²+6x
f''(x)=-6x+6
当-6x+6＞0时,x＜1
当-6x+6＜0时,x＞1
f(1)=-5
f(x)的拐点是(1,-5)
当x＜1时,f(x)下凹,当x＞1时,f(x)上凹
f'(1)=3
设切线方程为y=3x+b
代入点(1,-5),解得b=-8
f(x)在拐点P上有穿过曲线的切线y=3x-8

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