一道高数题 Find A and B given that the function f(x) is differentiable at x=1f(x)= x^3 (x1)
问题描述：
一道高数题 Find A and B given that the function f(x) is differentiable at x=1
f(x)= x^3 (x1)
答
可导必连续，先利用连续，A+B = 1 => B=1-A
在x=1 求出：左导数 f '-(1) = 3, 右导数 f '+(1) = A,
=》 A=3, B = -2
答
因为可导所以在x=1时两个表达式极限相同,两个表达式的导数的极限也相同,即：
lim f(x) at x=1 gives
1^3=A*1+B => A+B=1
lim f'(x) at x=1 gives
3*1^2=A => A=3, so B=-2