二西安毛子律技大学2xen(x-1) + ax + b例3. 设f(x)= limen(x-1) +1n-0试确定常数a,b使,f(x)处处可导,并求f'(x)ax+b,x<1解: f(x)=^ (a+b+1),x=1x2.x>1x<1时,f(x)=a; x>1时,f'(x)=2x利用f(x)在x=1处可导，得α+b =1=(α+b+1)f(1t)= f(1)= f(1)即a= 2f'(1) = f*(1)66 例3. 设 试确定常数 a , b 使 f (x) 处处可导,并求 解: f (x) = ax + b , x  1 ( 1), x = 1 2 1 a+ b + , x  1 2 x x  1时, f (x) = a ; x  1时，f (x) = 2x. (1) (1) − + f  = f  利 用 f (x)在 x = 1处可导， 得 即 a + b = 1 ( 1) 2 1 = a + b + a = 2 f f f (1 ) (1 ) (1) + − = =