f(x)=ax^2
f'(x)=2ax
依題意f'(1)=2a=2 解得a=1
拋物線方程f(x)=x^2
(1,-3)不在拋物線上
切點(diǎn)在拋物線上,設(shè)切點(diǎn)為(x0,x0^2)
(x0^2-(-3))/(x0-1)=2x0
x0^2+3=2x0^2-2x0
x0^2-2x0-3=0
(x0+1)(x0-3)=0
解得兩切點(diǎn)為(-1,1) (3,9)
點(diǎn)斜式
(y-1)/(x-(-1))=-2
y=-2x-1
(y-9)/(x-3)=6
y=6x-9
即切線方程為y=-2x-1或y=6x-9