Question

設(shè)f(x)，g(x)在[a，b]上可導(dǎo)，且f′(x)>g′(x)，則當(dāng)a<x<b時(shí)，有(  )

A．f(x)>g(x)

B．f(x)<g(x)

C．f(x)＋g(a)>g(x)＋f(a)

D．f(x)＋g(b)>g(x)＋f(b)

Answer 1

C

設(shè)F(x)＝f(x)－g(x)，則F′(x)＝f′(x)－g′(x)>0，即F(x)在[a，b]上是增函數(shù)，從而當(dāng)a<x<b時(shí)，f(x)－g(x)>f(a)－g(a)，即f(x)＋g(a)>g(x)＋f(a)，故選C.