Question

一道高数的基本导数题？

求解

Answer 1

f(1)=f(1+) = lim(x->1+) (x^2+1) =2

f(1-)=lim(x->1-) (ax+b) = a+b
a+b=2 (1)
f'(1+)
=lim(h->0) [((1+h)^2+1) -f(1) ]/h
=lim(h->0) [((1+h)^2+1) -2 ]/h
=lim(h->0) ( 2+h)
=2
f'(1-)
=lim(h->0) [a(h+1)+b -f(1) ]/h
=lim(h->0) [a(h+1)+b -2 ]/h
=lim(h->0) [ah+(a+b -2)]/h
=2
=>a=2

from (1)
a+b=2
b=0
(a,b)=(2,0)