f(0) = e^(-b)
切线上, x = 0, y = 4, e^(-b) = 4, b = -2ln2
f'(x) = ae^(ax - b) - 2x - 4
f'(0) = ae^(-b) - 4 = 4 (切线斜率)
4a - 4 = 4
a = 2
(2)
f(x) = e^(2x + 2ln2) - x^2 - 4x = 4e^(2x) - x^2 - 4x
f'(x) = 8e^(2x) - 2x - 4 = 0
没有容易解法.但容易看出,x ->负无穷时,e^(2x) -> 0, f(x)行为与-x^2 - 4x类似, 为增函数；
x -> 正无穷时,e^(2x) -> 0, f(x)行为与e^(2x)类似, 为增函数；
作图:
极大值约为f(-1.93) = 4.01
极小值约为f(-0.49) = 3.20
